Question

Prove that DE is parallel to BC. Please help, will award brainliest.

Answer 1

Answer:

see explanation

Step-by-step explanation:

Parallel lines have equal slopes.

To find D and E use the midpoint formula

Given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is

( $\frac{x_{1}+x_{2} }{2}$, $\frac{y_{1}+y_{2} }{2}$ )

Here (x₁, y₁ ) = A(4, 6) and (x₂, y₂ ) = B(2, - 2) , then

D = ($\frac{4+2}{2}$, $\frac{6-2}{2}$ ) = (3, 2 ) and

let (x₁, y₁ ) = B(2, - 2$\frac{-4+2}{-2-2}$ ) and (x₂, y₂ ) = C(- 2, - 4 ), then

E = ( $\frac{4-2}{2}$, $\frac{6-4}{2}$ ) = (1, 1 )

Use the slope formula to find slopes of DE and BC

m = $\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$

with (x₁, y₁ ) = D(3, 2) and (x₂, y₂ ) = E(1, 1), then

$m_{DE}$ = $\frac{1-2}{1-3}$ = $\frac{-1}{-2}$ = $\frac{1}{2}$

Repeat with (x₁, y₁ ) = B(2, - 2) and (x₂, y₂ ) = C(- 2, - 4), then

$m_{BC}$ = $\frac{-4+2}{-2-2}$ = $\frac{-2}{-4}$ = $\frac{1}{2}$

Since the slopes are equal then DE and BC are parallel lines

Answer 2

Anwser


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