Answer:
The coordinates of point S are (5, 9) will make line PQ // line RS ⇒ A
Step-by-step explanation:
<em>Parallel lines have the same slopes</em>
The slope of a line = Δy/Δx, where
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
