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
Since ∠1 and ∠2 are complementary...they add up to be 90°.
∠1 = (-2x + 54)
∠2 = (8x + 18) we add these two up
6x + 72 = 90 subtract 72 from both sides
6x = 18
x = 3 place the value of x into the ∠2 equation
(8x + 18) = 8(3) + 18 = 24 + 18 = ∠2 = 42°
I’m pretty sure you set the perimeters equal to each other, it would look like 3x+8+3x+7+3x = 3x+3x+4x+2 and then you add the similar ones so it would look like 9x+15 = 10x+2 then you subtract the two from both sides and subject the 9x from both sides and get 13 = x
AB would be 47
BC = 46
AC = 39
PQ = 39
QR = 39
PR = 54
then you could double check
47+46+39 = 39+39+54
132 = 132
