Question

Rectangle TUVW is on a coordinate plane at T (a,b),U(a+2,b+2),V(a+5,b-1), and W (a+3,b-3). What is the slope of the line that is parallel to the line that contains side UV

Answer 1

Answer:

slope = - 1

Step-by-step explanation:

Parallel lines have equal slopes.

Thus the slope of TW equals the slope of UV

Calculate the slope m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = U(a + 2, b + 2) and (x₂, y₂ ) = V(a + 5, b - 1)

m = $\frac{b-1-(b+2)}{a+5-(a+2)}$ ← distribute and simplify numerator/ denominator

   = $\frac{b-1-b-2}{a+5-a-2}$

   = $\frac{-3}{3}$ = - 1