Question

Which point on the x-axis lies on the line that passes through point C and is parallel to line AB?

a (1,0)
b (1,1)
c (0,2)
d (2.0)​

Answer 1

d. (2, 0)

Explanation:

Parallel lines have the same slope.

The formula of a slope:

`m=(y_2-y_1)/(x_2-x_1)`

We have the points A(-4, 0) and B(2, -3). Substitute:

`m=(-3-0)/(2-(-4))=(-3)/(6)=-(1)/(2)`

C(-2, 2).

The point on the x-axis D(x , 0).

The slope:

`m=(0-2)/(x-(-2))=(-2)/(x+2)`

Put the value of the slope:

`(-2)/(x+2)=(-1)/(2)` change the signs

`(2)/(x+2)=(1)/(2)` cross multiply

`x+2=(2)(2)`

`x+2=4` subtract 2 from both sides

`x=2`