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

Answer: D (2,0)

Explanation:

Answer 2

Option D.

Explanation:

Consider the below figure attached with this question.

From the below figure it is clear that the coordinates of given points are A(-4,0), B(2,-3) and C(-2,2).

Slope of line AB is

`m_(AB)=(y_2-y_1)/(x_2-x_1)=(-3-0)/(2-(-4))=-(1)/(2)`

The slope of two parallel lines are same.

So, the slope of required line is -1/2.

The point slope form of a line is

`(y-y_1)=m(x-x_1)`

where, m is slope.

The equation of required line is

`(y-2)=-(1)/(2)(x-(-2))`

`2(y-2)=-(x+2)`

`2y-4=-x-2`

`x+2y-2=0`

Substitute y=0 in the above equation to find the x-intercept of required line.

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

`x-2=0`

`x=2`

The x-intercept of required line is (2,0). Therefore, the correct option is D.