Question

Find the lengths and slopes of the diagonals to name the parallelogram. Choose the most specific name.

E(-2, -4), F(0, -1), G(-3, 1), H(-5, -2)


Find the lengths and slopes of the diagonals to name the parallelogram. Choose the most specific name.

E(-2, -4), F(0, -1), G(-3, 1), H(-5, -2)


Triangle

Rectangle

Rhombus

Square

Answer 1

To determine the lengths and slopes of the diagonals, we need to find the distances between the points and the slopes of the lines connecting them:

Diagonal EG:
Length: √((-3 - (-2))^2 + (1 - (-4))^2) = √2^2 + 5^2 = √4 + 25 = √29
Slope: (1 - (-4))/(-3 - (-2)) = 5/-1 = -5

Diagonal FH:
Length: √((-5 - 0)^2 + (-2 - (-1))^2) = √5^2 + 1^2 = √25 + 1 = √26
Slope: (-2 - (-1))/(-5 - 0) = -1/-5 = 1/5

Since the diagonals have different lengths and slopes, the parallelogram formed by the points E, F, G, and H is a **parallelogram** without a more specific name.