Question

Which triangle would be most helpful in finding the distance between the points (–4, 3) and (1, –2) on the coordinate plane?

On a coordinate plane, a triangle has points (negative 4, 3), (1, negative 2), (5, 3).
On a coordinate plane, a triangle has points (negative 4, 2), (negative 1, 4), (1, negative 3).
On a coordinate plane, a triangle has points (negative 4, 3), (negative 4, negative 2), (1, negative 2).
On a coordinate plane, a line is drawn between points (negative 4, negative 3) and (negative 1, 4).

Answer 1

The triangle with vertices (-4, 3), (-4, -2), and (1, -2).

Reason: This makes a right triangle with horizontal leg length |1 - (-4)| = 5 and vertical leg length |3 - (-2)| = 5, so the distance between (-4, 3) and (1, -2) is the hypotenuse:
sqrt(5^2 + 5^2) = sqrt(50) = 5√2.