Question

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

Answer 1

Answer:

Option D.

Step-by-step 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

$m_{AB}=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-3-0}{2-(-4)}=-\dfrac{1}{2}$

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

$(y-2)=-\dfrac{1}{2}(x-(-2))$

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

$2y-4=-x-2$

$x+2y-2=0$

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.