Question

On a coordinate plane, a line and a point are shown. Line G H has points (negative 4, 1) and (2, negative 2). Point J is at (1, 3).

Which points could be on the line that is parallel to Line G H and passes through point J? Check all that apply.

(–3, 5)
(1, 5)
(3, −2)
(3, 2)
(5, 1)

Answer 1

Slope of GH = (-2 − 1)/(2 − (−4)) = −3/6 = −1/2. The line through J(1,3) with slope −1/2 has equation y − 3 = −(1/2)(x − 1).

Check each point (or check the vector from J):
- (−3, 5): vector (−4, 2) → slope 2/−4 = −1/2 ✓
- (1, 5): vector (0, 2) → undefined/0 ≠ −1/2 ✗
- (3, −2): vector (2, −5) → slope −5/2 ≠ −1/2 ✗
- (3, 2): vector (2, −1) → slope −1/2 ✓
- (5, 1): vector (4, −2) → slope −1/2 ✓

Correct points: (−3, 5), (3, 2), (5, 1).