Question

*30 points* Consider the figure shown on the coordinate plane. What are the coordinates of the midpoint of line segment AC?

A) -2, -1
B) 4, 0
C) -1, 1
D) -1, -1

Answer 1

Midpoint of AC = (–1, –1)

Solution:

In the given graph we can find the coordinates of A and C.

Coordinates of A = (–4, 2)

Coordinates of C = (2, –4)

Here,
`x_1=-4,x_2=2,y_1=2,y_2=-4`

Let us find the midpoint of the segment AC.

Midpoint formula:

`$\text{Midpoint} =\left((x_1+x_2)/(2), (y_1+y_2)/(2)\right)`

`$=\left((-4+2)/(2), (2-4)/(2)\right)`

`$=\left((-2)/(2), (-2)/(2)\right)`

`$=(-1, -1)`

Midpoint of AC = (–1, –1)

Option D is the correct answer.

Hence the coordinates of the midpoint of the line segment AC is (–1, –1).