Free Printable ACTIVITY: MODERN GEOMETRY 2025

1.

Who is the father of geometry?

a)

René Descartes

b)

Fibonacci

c)

Euclid of Alexadria

d)

Pythagoras

2.

What refers to a mathematical statement that is regarded as “self-evident” and accepted without proof?

a)

formula

b)

axiom

c)

theorem

d)

fact

3.

What refers to a set of infinitely many points that extend forever in both directions?

a)

line

b)

point

c)

ray

d)

line segment

4.

Any two right angles are __________.

a)

congruent

b)

perpendicular

c)

parallel

d)

opposite

5.

If AB = CD, CD = EF and EF =PQ then which one of the following is not true?

a)

AB = PQ

b)

CD = PQ

c)

AB=EF

d)

AB is not equal to CD

6.

Euclid's axiom 1 is

a)

Things which are equal to the same thing are equal to one another

b)

If equals are added to equal then wholes are equal

c)

Given two distinct points there is a unique line that passes through them

d)

None of these

7.

In the given figure if AB = BC and BX = BY,then

a)

AX = CY

b)

AC = XY

c)

AY = CX

d)

None of these

8.

All right angles are equal to one-another.

a)

Axiom

b)

Postulate

9.

The whole is greater than the part.

a)

Axion

b)

Postulate

10.

The hyperbolic axiom states that through a point not on a given line, more than two lines can be drawn that do not intersect the given line.

a)

True

b)

False

11.

The elliptic axiom states that two lines always intersect.

a)

True

b)

False

12.

What type of triangle is this

a)

Elliptic Geometry

b)

Hyperbolic Geometry

c)

Euclidean Geometry

13.

What is the total number of lines is four-line geometry?

a)

2

b)

3

c)

4

d)

5

14.

In four-line geometry, how many points does each line contain?

a)

2

b)

3

c)

4

d)

8

15.

Which French mathematician is considered one of the founders of projective geometry?

a)

Blaise Pascal

b)

Pierre de Fermat

c)

Girard Desargues

d)

René Descartes

16.

The theorem of Pappus and Guldinus is used to find the ____________

a)

Surface area of the body

b)

Surface area of the body of revolution

c)

Surface area of the body of linear motion

d)

Surface area of the body of rectangular motion

17.

How many lines and point are elements of Desargues triangle?

a)

3

b)

7

c)

10

d)

12

18.

If two triangles are perspective to a point it is also perspective to a?

a)

Line

b)

Triangle

c)

Point

d)

Perspective

19.

Which axiom states that there exist at least 1 point?

a)

Axiom 1

b)

Axiom 2

c)

Axiom 3

d)

Axiom 4

20.

Is this an example of finite geometry of Desargues?

a)

Yes

b)

No

21.

Is this an example of finite geometry of Desargues?

a)

Yes

b)

No

22.

Is this an example of finite geometry of Desargues?

a)

Yes

b)

No

23.

Is this an example of finite geometry of Desargues?

a)

Yes

b)

No

24.

How many triangles are perspective to a point and a line in the finite geometry of Desargues?

a)

2

b)

3

c)

7

d)

10

25.

Is this an example of finite geometry of Desargues?

a)

Yes

b)

No

26.

How many distinct lines and points in Pappus's geometry configuration?

a)

8

b)

9

c)

10

d)

6

27.

What are the equations for the two lines shown here?

a)

$y\ =\ 2x$ and $x\ =\ 0$

b)

$null$ and $y\ =0$

c)

$y\ =\ 2$ and $x\ =\ 0$

d)

$y\ =\ 0$ and $x\ =\ 2$

28.

What is the slope of the line that passes through these two points (0, -2) and (3, -4)?

a)

2/3

b)

-2/3

c)

3

d)

-2

29.

What is the equation of a line with a slope of 4 and a y-intercept of 2?

a)

y = -4x + 2

b)

y = -2x + 4

c)

y = 4x + 2

d)

y = 2x + 4

30.

If m=3 and b=6, what is the correct slope intercept equation?

a)

y=3-6

b)

y=3x-6

c)

y=3x+6

d)

y=6x+3

31.

Write the equation of the line.

a)

y = -1/3x - 2

b)

y = 1/3x - 2

c)

y = 3x - 2

d)

y = -3x - 2

32.

Write the equation of the line.

a)

y = -2/3x + 4

b)

y = 2/3x + 4

c)

y = 3/2x + 4

d)

y = -3/2x + 4

33.

Find the slope of the line.

a)

1/2

b)

-1/2

c)

2

d)

-2

34.

Slope is know as rise/

a)

run

b)

fall

c)

none

d)

rise

35.

Determine the slope and y-intercept from the following equation: y = 3/2x + 3

a)

slope: 5 y-intercept: (0,3)

b)

slope: 3/2 y-intercept: (0,3)

c)

slope: 4 y-intercept: (0,3/2)

d)

slope: 1/5 y-intercept: (0,5)

36.

Solve this equation for y:
$-6x+3y=9$

a)

y = 2x + 9

b)

y = 6x - 3

c)

y = 2x + 3

d)

y = 6x + 9

37.

Which could be the graph of the equation y = 1/3x - 2?

a)

b)

c)

d)

38.

Which graph best represents the equation y = -3x + 4?

a)

b)

c)

d)

39.

Which is the graph of y= -x + 2?

a)

A

b)

B

c)

C

d)

D

40.

what is the slope of the following 12x - 6y = 30

a)

2

b)

-2

c)

12

d)

-12

41.

Find the distance between ( 1, 3) and (5, 6)

a)

3

b)

4

c)

5

d)

6

42.

Write the equation $6x+8y\ =\ 4x+4y+6$ in standard form

a)

$2x+4y=6$

b)

$2x-4y=6$

c)

$2x+4y+6=0$

d)

$2x-4y-6=0$

43.

In the equation 2x + 3y = 6, what is the y-intercept?

a)

(2 ,0)

b)

(0 ,3)

c)

(3 ,0)

d)

(0, 2)

44.

Convert from Standard Form to Slope-Intercept Form.

$6x-y=1$

a)

$y=-6x+1$

b)

$y=6x-1$

c)

$y=\frac{1}{6}x-1$

d)

$y=-6x+1$

45.

Which equation matches the graph? (Click me to see the image)

a)

$y=-\frac{1}{4}x+2$

b)

$y=\frac{1}{4}x+2$

c)

$y=x+4$

d)

$y=4x+2$

46.

Find the direction of the vector given the points A=(1,2) B=(5,4)

a)

(1,2)

b)

(5,4)

c)

(4,2)

d)

(2,4)

47.

A vector of length 1 is said to be a unit vector. A pair (u,w) of unit orthogonal vectors.

a)

Orthogonal pair

b)

Orthonormal pair

c)

Orthonormal base

d)

Normal vector

48.

A=(1,2), the direction vector (3,4)

Find the equation of the line.

a)

$4x-3y+2=0$

b)

$x+y+4=0$

c)

$y=\frac{4}{3}x+2$

d)

$x=\frac{3}{4}y+2$

49.

The parametric equation of the line given points P and Q is:

a)

$\alpha\left(t\right)=P+t\left(Q-P\right)$

b)

$\alpha\left(t\right)=P+t\left(Q+P\right)$

c)

$\alpha\left(t\right)=P-t\left(Q-P\right)$

d)

$\alpha\left(t\right)=P+\alpha\left(Q-P\right)$

50.

Identify the transformation from ABC to A'B'C'.

a)

90^o clockwise rotation

b)

90^o counter clockwise rotation

c)

Reflection across the y-axis

d)

Reflection across the x-axis

ACTIVITY: MODERN GEOMETRY 2025

Total questions: 50

Worksheet time: 50mins

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