Free Printable Geo9.1 Coordinate Geometry- Triangles and Quadrilaterals

1.

Given the points $A(1,2)$ , $B(4,6)$ , and $C(7,2)$ , what type of triangle is $\triangle ABC$ based on its side lengths?

a)

Equilateral

b)

Isosceles

c)

Scalene

d)

Right-angled

2.

The vertices of a triangle are $A(0,0)$ , $B(4,0)$ , and $C(2,3)$ . What is the classification of $\triangle ABC$ ?

a)

Right-angled triangle

b)

Equilateral triangle

c)

Isosceles triangle

d)

Scalene triangle

3.

Given the points $A(1,1)$ , $B(5,1)$ , $C(5,4)$ , and $D(1,4)$ , what type of quadrilateral is $ABCD$ ?

a)

Parallelogram

b)

Rectangle

c)

Rhombus

d)

Trapezium

4.

Which of the following sets of points forms an isosceles triangle?

a)

$A(0,0)$ , $B(2,0)$ , $C(1,2)$

b)

$A(0,0)$ , $B(3,0)$ , $C(1.5,2)$

c)

$A(0,0)$ , $B(2,0)$ , $C(2,2)$

d)

$A(0,0)$ , $B(1,1)$ , $C(2,0)$

5.

The points $A(2,3)$ , $B(6,3)$ , $C(6,7)$ , and $D(2,7)$ are the vertices of a quadrilateral. What is the most specific name for this quadrilateral?

a)

Square

b)

Rectangle

c)

Parallelogram

d)

Rhombus

6.

Given $A(0,0)$ , $B(4,0)$ , $C(2,2\sqrt{3})$ , what type of triangle is $\triangle ABC$ ?

a)

Equilateral

b)

Isosceles

c)

Scalene

d)

Right-angled

7.

Which of the following quadrilaterals has only one pair of parallel sides?

a)

Rectangle

b)

Parallelogram

c)

Trapezium

d)

Rhombus

8.

The points $A(1,2)$ , $B(4,6)$ , $C(7,2)$ , and $D(4,-2)$ form a quadrilateral. What is the most specific classification for $ABCD$ ?

a)

Square

b)

Rectangle

c)

Rhombus

d)

Parallelogram

9.

If the slopes of two sides of a triangle are negative reciprocals, what does this indicate about the triangle?

a)

It is equilateral

b)

It is isosceles

c)

It has a right angle

d)

It is scalene

10.

Given $A(0,0)$ , $B(2,2)$ , $C(4,0)$ , what type of triangle is $\triangle ABC$ ?

a)

Right-angled

b)

Isosceles

c)

Equilateral

d)

Scalene

11.

Which of the following sets of points forms a square?

a)

$A(0,0)$ , $B(2,0)$ , $C(2,2)$ , $D(0,2)$

b)

$A(0,0)$ , $B(3,0)$ , $C(3,2)$ , $D(0,2)$

c)

$A(1,1)$ , $B(4,1)$ , $C(4,5)$ , $D(1,5)$

d)

$A(0,0)$ , $B(1,2)$ , $C(3,2)$ , $D(2,0)$

12.

The points $A(0,0)$ , $B(2,2)$ , $C(4,0)$ , and $D(2,-2)$ form which type of quadrilateral?

a)

Rectangle

b)

Rhombus

c)

Square

d)

Parallelogram

13.

If the diagonals of a quadrilateral bisect each other, what type of quadrilateral is it?

a)

Trapezium

b)

Parallelogram

c)

Kite

d)

Rectangle

14.

Given $A(0,0)$ , $B(4,0)$ , $C(2,2)$ , what is the area of $\triangle ABC$ ?

a)

$4$

b)

$6$

c)

$8$

d)

$2$

15.

Which property is true for all rectangles but not for all parallelograms?

a)

Opposite sides are equal

b)

Diagonals bisect each other

c)

All angles are right angles

d)

Opposite sides are parallel

16.

The points $A(0,0)$ , $B(2,3)$ , $C(5,3)$ , and $D(7,0)$ form a quadrilateral. What is the most specific classification for $ABCD$ ?

a)

Parallelogram

b)

Rectangle

c)

Trapezium

d)

Rhombus

17.

1. How is a coordinate proof different from other types of proofs you have studied?

a)

You do not need to write a plan for a coordinate proof.

b)

You do not have a Given or Prove statement.

c)

You have to assign coordinates to vertices and write expressions for the side lengths and slopes of segments.

d)

You can only do coordinate proofs with triangles.

18.

2. Explain why it is convenient to place a right triangle on the grid as shown when writing a coordinate proof.

a)

The hypotenuse of the right triangle is easy to identify.

b)

The side lengths are often easier to find because you are using zeros in your expressions.

c)

It is easier to dilate the figure on the coordinate plane.

d)

Both legs have the same length when you place the triangle on the x- and y-axes.

19.

Select the graph that represents an isosceles right triangle with leg length p in the most convenient way.

a)

b)

c)

d)

20.

Select the most convenient graph to represent a scalene triangle with one side length of 2m.

a)

b)

c)

d)

21.

Write a plan for the proof.

Given Coordinates of vertices of △OPM and △ONM

Prove △OPM and △ONM are isosceles triangles

a)

Find the lengths of OP, PM, MN, NO and OM using the distance formula to show that △OMP≅△OMN by the SSS Congruence Theorem.

b)

Find the lengths of OP, PM, MN, and NO using the distance formula to show that OP ≅ PM and MN ≅ NO.

22.

Write a plan for the proof.

Given: G is the midpoint of HF
Prove: △GHJ≅△GFO

a)

Find the coordinates of G using the Midpoint Formula
Use these coordinates and the Distance formula to show that OG ≅ JG.
Show that HG≅ FG by the definition of midpoint and ∠HGJ ≅ ∠FGO by the Vertical Angles Congruence Theorem.

b)

Find the coordinates of G using the Distance Formula
Use these coordinates and the Midpoint formula to show that OG ≅ JG.
Show that HG≅ FG by the definition of midpoint and ∠HGJ ≅ ∠FGO by the Vertical Angles Congruence Theorem.

c)

Then, use the SAS Congruence Theorem to conclude that △GHJ ≅ △GFO.

d)

Then, use the SSS Congruence Theorem to conclude that △GHJ ≅ △GFO.

23.

Find the coordinates of the vertex O.

(a)

24.

Find the coordinates of the vertex U.

a)

(k, 0)

b)

(0, k)

c)

(k, 2k)

d)

(2k, k)

25.

a)

Find the slope of two consecutive sides.

b)

Find the slope of all 4 sides.

c)

Find the slope of the diagonals.

d)

Find the length of two consecutive sides.

26.

a)

Find the length of all 4 sides.

b)

Find the length of both diagonals.

c)

Find the slope of both diagonals

d)

Find the slope of all 4 sides.

27.

a)

Find the slope of any 2 consecutive sides.

b)

Find the length of all 4 sides.

c)

Find the slope of all 4 sides.

d)

Find the midpoint of all 4 sides.

28.

a)

Find the midpoint of the diagonals.

b)

Find the length of the diagonals.

c)

Find the slope of the diagonals.

d)

Diagonals in a rhombus are not perpendicular, so this is not a good method.

29.

If given the coordinates of a quadrilateral, using the distance formula to find the lengths of the diagonals will allow you to prove if it is a parallelogram.

a)

True, if they're congruent then it's a parallelogram

b)

True, if they're congruent then it's a rectangle

c)

False, you should find the opposite sides' slopes for it to be a parallelogram

d)

False, you should find the opposite sides' slopes for it to be a rhoombus

30.

Which statement is sufficient to prove that quadrilateral ABCD is a parallelogram?

a)

One pair of sides is congruent

b)

One pair of sides is parallel

c)

The diagonals are perpendicular

d)

The diagonals bisect each other

31.

Julia proved ETNU is a parallelogram. She notices that side ET has a slope of 1/2 and EN has a slope of -2. What does this mean?

a)

Side ET and EN are parallel

b)

Side ET and EN form a right angle

c)

Side ET and EN are congruent

d)

Nothing Specific

32.

Determine the type of quadrilateral formed by the points (0, 0), (4, 0), (4, 4), and (0, 4).

a)

Square

b)

Trapezoid

c)

Rhombus

d)

Rectangle

33.

Identify the properties of a parallelogram using the coordinates of its vertices.

a)

Sum of all angles is 180 degrees

b)

Distance and slope of opposite sides are equal

c)

Opposite sides are congruent

d)

Diagonals are perpendicular

34.

Find the coordinates of the midpoint of the line segment with endpoints (-3, 5) and (7, -3).

a)

(-3, 5)

b)

(7, -3)

c)

(5, -3)

d)

(2, 1)

35.

What is the perimeter of the shaded figure?

a)

28

b)

24

c)

22

d)

26

36.

What is the area of the figure plotted on the coordinate grid?

a)

20 units2

b)

14 units2

c)

10 units2

d)

15 units2

37.

Which statement best explains why ABCD is a parallelogram?

a)

slope of AB = slope of CD = 0; slope of BC = slope of AD = 5/3.

b)

BC = AD = 8; AB = CD = 14

c)

slope of AB = slope of CD = 0; slope of BC = slope of AD = 2

d)

BC = AD = 10; AB = CD = 18

38.

What is the perimeter of the rectangle?

a)

9.75 units

b)

13.5 units

c)

16 units

d)

60 units

39.

What is the perimeter of the composite figure?

a)

78 units

b)

90 units

c)

114.75 units

d)

125.5 units

40.

Which statement is true about this polygon? Select all that apply.

a)

The polygon has a perimeter of 22 units.

b)

The polygon has a perimeter of 88 units.

c)

The polygon has 2 pairs of parallel sides.

d)

The polygon has 4 congruent sides.

41.

Quadrilateral ABCD is shown on the grid. Jonah finds the length of the sides of the quadrilateral before finding the perimeter. Which statement is true about the length of the sides of quadrilateral ABCD?

a)

Side CD has a length of $\sqrt{5}$ units.

b)

Side BC has a length of $\sqrt{10}$ units.

c)

Side DA has a length of 5 units.

d)

Side AB has a length of 6 units.

42.

Jerome found the lengths of each side of triangle QRS as shown, but did not simplify his answers. Simplify the lengths of each side to answer the question. Which statement about triangle QRS is true?

a)

Triangle QRS is an equilateral triangle because QR = RS.

b)

Triangle QRS is an isosceles triangle because QR = QS.

c)

Triangle QRS is a scalene triangle because all sides have different lengths.

d)

Triangle QRS is an isosceles triangle because QR = RS.

43.

Point A has an x coordinate of −2 and lies in a circle with a center at (0, 0) and a radius of 5. To the nearest tenth, what is the y-coordinate for point A?

a)

4.5

b)

4.6

c)

4.7

d)

4.8

44.

HIJK is a parallelogram because the midpoint of both diagonals is __________, which means the diagonals bisect each other.

a)

(1, -1)

b)

(1, 1)

c)

(1, 0)

d)

(0, 1)

45.

Which statement proves that PQRS is a parallelogram?

a)

The slopes of SP and RQ are both –2 and SP = RQ = $\sqrt{45}$ .

b)

The slopes of RS and QP are both 3 and SP = RQ = $\sqrt{45}$ .

c)

The midpoint of RP is (4, 5 1/2) and the slope of RP is -9/2.

d)

The midpoint of SQ is (4, 5 1/2) and SQ = 5.

46.

What is the perimeter of kite KLMN?

a)

$\sqrt{2}+\sqrt{5}\ units$

b)

$\sqrt{14}\ units$

c)

$2\sqrt{2}+2\sqrt{5}\ \ units$

d)

$4\sqrt{5}\ \ units$

47.

What is the perimeter of parallelogram WXYZ?

a)

$\sqrt{5}+\ \sqrt{17}\ \ units$

b)

$2\sqrt{5}+\ 2\sqrt{17}\ \ units$

c)

16 units

d)

22 units

48.

In the diagram, WZ = $\sqrt{26}$ . What is the perimeter of parallelogram WXYZ?

a)

$2\sqrt{26}+\ 2\ units$

b)

$2\sqrt{26}+\ 4\ units$

c)

$2\sqrt{26}+\ 6\ units$

d)

$2\sqrt{26}+\ 8\ units$

49.

What is the perimeter of square ABCD?

a)

$\sqrt{37}\ units$

b)

$4\sqrt{37}\ units$

c)

28 units

d)

37 units

50.

Find the coordinates of the midpoint of the line segment with endpoints (2, 4) and (6, 8).

a)

(3, 5)

b)

(5, 10)

c)

(1, 3)

d)

(4, 6)

51.

Identify the type of triangle formed by the points (-1, 0), (3, 4), and (5, 2).

a)

Isosceles triangle

b)

Right-angled triangle

c)

Equilateral triangle

d)

Scalene triangle

52.

Determine the type of quadrilateral formed by the points (0, 0), (4, 0), (4, 4), and (0, 4).

a)

Square

b)

Trapezoid

c)

Rhombus

d)

Rectangle

53.

Identify the properties of a parallelogram using the coordinates of its vertices.

a)

Sum of all angles is 180 degrees

b)

Distance and slope of opposite sides are equal

c)

Opposite sides are congruent

d)

Diagonals are perpendicular

54.

Give the most precise classification for the quadrilateral.

a)

parallelogram

b)

rhombus

c)

square

d)

rectangle

e)

kite

55.

Give the most precise classification for the quadrilateral.

a)

parallelogram

b)

rhombus

c)

kite

d)

rectangle

56.

If the lines are parallel to each other and the slope of the blue line is 1/4, what is the slope of the purple line?

a)

4

b)

-4

c)

$-\frac{1}{4}$

d)

$\frac{1}{4}$

57.

If the lines are perpendicular to each other and the slope of the blue line is $\frac{1}{2}$ , what is the slope of the purple line?

a)

2

b)

-2

c)

$-\frac{1}{2}$

d)

$\frac{1}{2}$

58.

Slopes of parallel lines are...

a)

opposite reciprocals

b)

the same

c)

opposites

d)

always 7

59.

Fill in the blanks:
Point (0 , -7) lies______

a)

on the x-axis

b)

in the second quadrant

c)

on the y-axis

d)

in the fourth quadrant

60.

Abscissa of all the points on the x-axis is _____

a)

0

b)

1

c)

any number

d)

2

61.

The point at which the two coordinate axes meet is called ______

a)

abscissa

b)

ordinate

c)

origin

d)

quadrant

62.

If y-coordinate of a point is zero, then this point always lies:

a)

in I quadrant

b)

in II quadrant

c)

on x - axis

d)

on y - axis

63.

The point whose ordinate is 4 and which lies on y-axis is _____

a)

(4 , 0)

b)

(0 , 4)

c)

(1 , 4)

d)

(2, 4)

64.

Say 'TRUE' or 'FALSE'
Point (1 , -1) and (-1 , 1) lies in the same quadrant

a)

TRUE

b)

FALSE

65.

Name the quadrant in which the point (-5 , -4) lie

a)

I QUDRANT

b)

II QUADRANT

c)

III QUADRANT

d)

IV QUADRANT

66.

What is the mirror image of (3 , 9) on x-axis?

a)

(3 , -9)

b)

(9 , 3)

c)

(-9 , -3)

d)

(-3 , -9)

67.

The sign of x-coordinate of a point lying in the IV quadrant is

a)

+

b)

-

c)

±

d)

None of the above

68.

The figure obtained by plotting the points (2 ,3), (-2, 3), (-2, -3) and (2, -3) is _________

a)

Trapezium

b)

Rectangle

c)

Square

d)

Rhombus

69.

Which of the following could represent the missing coordinates of P in rectangle KPWA?

a)

(0, c)

b)

(x, y)

c)

(x, c)

d)

(c, c)

70.

Which point has the coordinates (0,6)

a)

A

b)

B

c)

C

d)

D

71.

Point (-3,5) lies in the

a)

First quadrant

b)

Second quadrant

c)

Third quadrant

d)

Fourth quadrant

72.

Point (0,-11) lies

a)

In the third quadrant

b)

On the negative y-axis

c)

On the positive x-axis

d)

On the fourth quadrant

73.

Sign of abscissa and ordinate of a point in the fourth quadrant are respectively

a)

+ , -

b)

- , -

c)

- , +

d)

+ , +

74.

Coordinate of origin is _______

a)

(0,0.1)

b)

(0,-6)

c)

(0,0)

d)

(-1,-1)

75.

What is the coordinate of P?

a)

(2 , -2)

b)

(4 ,3)

c)

(-2 ,3)

d)

(-4 , -2)

76.

What is the coordinate of R?

a)

(2 , -2)

b)

(4 ,3)

c)

(-2 ,3)

d)

(-4 , -2)

77.

What is the coordinate of S?

a)

(2 , -2)

b)

(4 ,3)

c)

(-2 ,3)

d)

(-4 , -2)

78.

What is the coordinate of Q?

a)

(2 , -2)

b)

(4 ,3)

c)

(-2 ,3)

d)

(-4 , -2)

79.

If abscissa is negative and ordinate is zero it will lie on third quadrant?

a)

True

b)

False

80.

The perpendicular distance of point (-4, 8) from x-axis is ?

a)

-8

b)

7

c)

8

d)

9

81.

Horizontal distance of point (5, 7) from origin is ?

a)

9

b)

6

c)

5

d)

7

82.

What shape is form when we join point (0,7) , ( 0,0) , (8,0)?

a)

Rectangle

b)

Triangle

c)

Square

d)

Parallelogram

83.

If (a ,8) lies on y-axis , then what is the value of a?

a)

8

b)

1

c)

0

d)

-8

84.

There are two point P(2,5) and Q(0,8) on the Cartesian plane, the longest perpendicular distance from x-axis will be the point

a)

Q

b)

Both have same distance

c)

P

85.

Suppose there are three points on cartesian plane if two points have abscissa negative and ordinate positive and the other point has ordinate positive and abscissa positive . Then how many point lies on second quadrant?

a)

One

b)

Two

c)

Zero

d)

Three

86.

Suppose there are three points on cartesian plane if two points have abscissa negative and ordinate positive and the other point has ordinate positive and abscissa positive . Then how many point lies on first quadrant?

a)

One

b)

Two

c)

Zero

d)

Three

87.

Suppose there are three points on cartesian plane if two points have abscissa negative and ordinate positive and the other point has ordinate positive and abscissa positive . Then how many point lies on fourth quadrant?

a)

One

b)

Two

c)

Zero

d)

Three

88.

Identify this person, who is also known as father of Geometry?

a)

Alexander Grothendieck

b)

René Descartes

c)

Évariste Galois

d)

Archimedes

89.

Signs of abscissa and ordinate of a point in the fourth quadrant are respectively

a)

+ , -

b)

- , -

c)

- , +

d)

+ , +

90.

A point lies on y-axis at a distance of 2 units from the x-axis .Its coordinates are (2,0)

a)

True

b)

False

91.

What error did the student make when plotting the point (3, 4) according to the picture?

a)

The student moved left along the x-axis when he should have moved right

b)

The student plotted the y-coordinate in place of the x-coordinate

c)

The student didn't make a mistake

92.

Which letter matches the coordinate (0, -6)?

a)

O

b)

L

c)

i

d)

Z

93.

What is the distance between points (3, -5) and (3, -8)?

a)

1 unit

b)

2 units

c)

3 units

d)

4 units

94.

The rectangle shown has coordinates (3, 2), (-2, 2), (-2, -1), (3, -1)

What is the length of the longest side of the rectangle?

a)

4 units

b)

5 units

c)

6 units

d)

8 units

95.

What is the area of the quadrilateral with vertices at (-1, 0), (2, 0), (2, 5), and (-1, 5)?

a)

15 square units

b)

12 square units

c)

10 square units

d)

5 square units

96.

What type of reflection does this picture show?

a)

reflection over the x-axis

b)

reflection over the x-axis, then the y-axis

c)

reflection over the y-axis

d)

reflection over the origin

97.

What is the reflection of F (3, 4) over the x-axis?

a)

F' (-3, -4)

b)

F' (3, -4)

c)

F' (-3, 4)

d)

F' (4, 3)

98.

If you reflect this point (-3, 1) across the x-axis then the y-axis, where would it be?

a)

(-3, -1)

b)

(3, -1)

c)

(3, 1)

d)

(1, -3)

99.

Use absolute value to find the distance between C(-4, 5) and E(-4,-1) ?

a)

5

b)

4

c)

6

d)

1

100.

What is the perimeter of the shape?

a)

20

b)

22

c)

24

d)

25

Geo9.1 Coordinate Geometry- Triangles and Quadrilaterals

Total questions: 100

Worksheet time: 5hrs 0mins

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