Question

A, B and C are the vertices of a triangle.

Answer 1

Answer:

Step-by-step explanation:

Use midpoint formula to find the coordinates of each midpoint.

(x, y) = (½ (x₁ + x₂), ½(y₁ + y₂))

Coordinates of D:

(x, y) = (½ (4 + 2), ½(6 + -2))

(x, y) = (3, 2)

Coordinates of E:

(x, y) = (½ (4 + -2), ½(6 + -4))

(x, y) = (1, 1)

Slope of DE:

m = Δy / Δx

m = (2 − 1) / (3 − 1)

m = 1/2

Slope of BC:

m = Δy / Δx

m = (-2 − -4) / (2 − -2)

m = 1/2

Therefore, DE is parallel to BC.

Answer 2

Answer:

Step-by-step explanation:

2/4=0.5

BC gradient is 2

AB (3,2)

AC (1,1)

DE gradient is 1/2=0.5

same gradients

parallel line have the same gradients

DE=0.5

BC=0.5

D has coordinate (3,2) and E has coordinate (1,1)

Gradient of DE = (2 - 1)/(3 - 1) = 0.5

Gradient of BC = (-2 - -4)/(3 - 1) = 0.5

BC and DE have the same gradient so they are parallel.