Question

Line PQ is located in the coordinate plane with point P at(-2,-2)

and point Q at (0,7). Point R is located at (3, 0). For what coordinates of point S will lines PQ and RS be parallel?
(5,9)
(9,5)
(5. – 1)
(1-1,5)

Answer 1

The coordinates of point S are (5, 9) will make line PQ // line RS ⇒ A

Explanation:

Parallel lines have the same slopes

The slope of a line = Δy/Δx, where

• Δ y is the change of y

• Δ x the change of x

Let us first find the slope of the line PQ.

∵ P = (-2, -2) and Q = (0, 7)

∴ Δx = 0 - (-2) = 0 + 2 = 2

∴ Δy = 7 - (-2) = 7 + 2 = 9

∴ The slope of PQ = 9/2

∵ Line PQ // line RS

∴ The slope of line PQ = the slope of line RS

∴ The slope of line RS =9/2

∵ Point R = (3, 0) and point S = (x, y)

∵ The slope of line RS = 9/2

∵ The slope = Δy/Δx

∴ Δy/Δx = 9/2

→ That means Δy = 9 and Δx = 2

∵ Δy = y - 0

∵ Δy = 9

∴ 9 = y

∵ Δx = x - 3

∵ Δx = 2

∴ 2 = x - 3

→ Add 3 to both sides

∴ 2 + 3 = x - 3 + 3

∴ 5 = x

∴ The coordinates of point S are (5, 9) will make line PQ // line RS