Free Printable Lines in the Coordinate Plane

1.

What is the length of the median passing through the vertex A of a triangle ABC with vertices A(4, 7), B(–1, 2), and C(3, 4)?

a)

5

b)

6

c)

7

d)

8

e)

10

2.

The distance of P(k, 1) to the line x – 2y + 2 = 0 is $2\sqrt{5}$ What is the sum of the possible values of k?

a)

-2

b)

-1

c)

0

d)

1

e)

2

3.

If the points A(–2, –1), B(2, k), and C(4, 5) are on the same line, what is k?

a)

1

b)

2

c)

3

d)

4

e)

5

4.

The centroid of ∆ABC with vertices A(–2, 1), B(1, 5), and C(4, –1) is on the line 2x + y + k – 1 = 0. Find k.

a)

$-1$

b)

$\frac{-1}{3}$

c)

$\frac{-5}{3}$

d)

$\frac{-8}{3}$

e)

$\frac{-10}{3}$

5.

A(–1, 2) and B(4, –3) are given. C is on the line
segment AB and $\frac{\left|AC\right|}{\left|BC\right|}=\frac{3}{5}$ .
What is the sum of the coordinates of C?

a)

1

b)

-1

c)

2

d)

-2

e)

3

6.

The points A(2, 1), B(2, 3), C(5, 4), and D(k, 1) are given. If AC ⊥ BD, what is k?

a)

-4

b)

-3

c)

-2

d)

3

e)

4

7.

The figure shows the graph of the height of a plant versus time in years. What is the height of the plant in the eighth year?

a)

9

b)

10

c)

12

d)

15

e)

20

8.

The point A(a ⋅ b, a – b) is in the second quadrant of the coordinate plane. In which quadrant is B(b2a, b – a)?

a)

$I$

b)

$II$

c)

$III$

d)

$IV$

e)

at the origin

9.

In the figure, P(0, k) is moving along the y-axis. A(3, 1) and B(4, 5) are given. Which value of k gives the smallest value of the sum PB + PA?

a)

$\frac{19}{7}$

b)

$\frac{17}{5}$

c)

$\frac{15}{4}$

d)

$\frac{13}{3}$

e)

$\frac{10}{3}$

10.

A(1, 2) and B(5, 4) are the endpoints of AB. The lines d: 3x + 4y – 12 = 0 and AB intersect at a point P. What is the ratio $\frac{PA}{PB}$ ?

a)

$\frac{1}{19}$

b)

$\frac{1}{17}$

c)

$\frac{1}{12}$

d)

$\frac{1}{8}$

e)

$\frac{1}{5}$

11.

Find the equation of the line parallel to the line 4x – 5y + 6 = 0 which intersects the line y – x – 3 = 0 on the y-axis.

a)

5y – 4x = 0

b)

2y – x + 6 = 0

c)

5y – 4x + 15 = 0

d)

5y – 4x – 15 = 0

e)

3y – x + 9 = 0

12.

Find the area of the triangle formed by the lines x + 2y – 4 = 0, 3x + 2y – 12 = 0, and the y-axis.

a)

8

b)

12

c)

16

d)

24

e)

32

13.

Which of the following lines has the greatest inclination?

a)

$2x-y+1=0$

b)

$x+2y-1=0$

c)

$y=5x+4$

d)

$y=\sqrt{3}x-1$

e)

$y=x+3$

14.

What is p, if the slope of the line 2px + (p –1)y + 1 = 0 is $\frac{-1}{2}$ ?

a)

$\frac{-1}{3}$

b)

$\frac{1}{2}$

c)

$\frac{1}{4}$

d)

$\frac{-1}{4}$

e)

$\frac{1}{5}$

15.

The lines $3x-ky+6=0\ and\ \left(k-5\right)x+2y-4=0$ are perpendicular. Find the value of k.

a)

15

b)

-15

c)

3

d)

-3

e)

2

16.

A point A(a, a-b) states in $IV.$ region in analytical plane. According to this which point will be in $III.$ region?

a)

$\left(b-a,\ b\right)$

b)

$\left(a+b,\ a-b\right)$

c)

$\left(-b,\ b-a\right)$

d)

$\left(-a,\ \frac{\left(a-b\right)}{b}\right)$

e)

$\left(b,\ a-b\right)$

17.

In the figure, AOBC is a rectangle. $d_1:\ y=2x\ and\ d_2:\ y=\frac{x}{2}$ , and A(0, 8) are given. What is the area of ∆COD?

a)

9

b)

12

c)

15

d)

18

e)

21

18.

A(–1, 3) and B(4, –2) are given. Find the equation of the line perpendicular to AB which passes through the origin.

a)

$x-y=0$

b)

$x+2y-1=0$

c)

$y=2x$

d)

$y=x-1$

e)

$y=\frac{x}{2}$

19.

The points A(1, –1), B(a, b), and C(–9, 9) are given. A, B, C are collinear and $\frac{AC}{BC}=\frac{5}{3}$ . Find the coordinates of B.

a)

(-3, 4)

b)

(-3, 3)

c)

(4, -3)

d)

(4, -4)

e)

(4, 5)

20.

A and B are the x- and y-intercept of the line x + 2y – 12 = 0, respectively. What is the equation of the median of the hypotenuse of the triangle formed by A, B, and the origin?

a)

$x-2y=0$

b)

$x+2y=0$

c)

$x-y=0$

d)

$2x+y=0$

e)

$y=3x$

Lines in the Coordinate Plane

Total questions: 20

Worksheet time: 59mins

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