The coordinates of quadrilateral PRAT are P(a, b), R(a, b + 3), A(a + 3, b + 4), and T(a + 6, b + 2). Prove that RA̅̅̅̅ is parallel to PT̅̅̅̅.

Question

The coordinates of quadrilateral PRAT are P(a, b), R(a, b + 3), A(a + 3, b + 4), and

T(a + 6, b + 2).

Prove that RA̅̅̅̅ is parallel to PT̅̅̅̅.

Answer 1

Hint: Parallel lines have the same slope so they never intersect. We can use the formula to find the slope.

Answer 2

Compute slope of RA:

((b+4) - (b+3))/((a+3) - a) = 1/3

Compute slope of PT:

((b+2) - b)/((a+6) - a) = 1/3

Slopes are identical, so two lines are parallel