Question

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

(1, 0)
(1, 1)
(0, 2)
(2, 0)

Answer 1

I don’t have the coordinates of A, B, and C or the diagram, so I can’t pick the correct choice yet. Could you give the coordinates of A, B, and C (or upload the diagram)?

If you want to solve it yourself, here is the method:

1. Find the slope of AB: m = (yB − yA)/(xB − xA).
- If AB is vertical (xB = xA), the line parallel to AB through C is x = xC, and its x-intercept is (xC, 0).
- If AB is horizontal (yB = yA), the parallel through C is y = yC. If yC ≠ 0 there is no x-intercept; if yC = 0 the whole line is on the x-axis.

2. If AB has finite nonzero slope m, the equation of the line through C(xC,yC) parallel to AB is y − yC = m(x − xC).

3. Set y = 0 to find the x-intercept:
0 − yC = m(x − xC) => x = xC − yC/m.

Plug in your A, B, C coordinates and compare the x-intercept to the choices given. If you provide the coordinates I’ll compute it.