Question

△abc has coordinates a(−2, 4) and b(−1, 1). choose all coordinates for vertex c that would make this a right triangle. (-2, 1) (-4, 1) (0, 4) (2, 2)

Answer 1

To determine which coordinate for vertex C turns triangle ABC into a right triangle, one must use the distance formula to find the lengths of the sides and apply the Pythagorean Theorem to check for a right angle.

Step-by-step explanation:

The question involves finding the coordinates for vertex C that would make triangle ABC a right triangle with the given coordinates of A(−2, 4) and B(−1, 1). To determine which of the given points makes triangle ABC a right triangle, we can apply the Pythagorean Theorem to check if one of the sides squared equals the sum of the other two sides squared.

We calculate the distance between two points using the distance formula d = √((x2 - x1)2 + (y2 - y1)2). Once we have the lengths of all three sides, we check for the Pythagorean Theorem by seeing if the square of the longest side (hypotenuse) is equal to the sum of the squares of the other two sides.

Without providing a complete walk-through of each potential coordinate for C, we can assess the options through calculation and verification to identify which makes the triangle right-angled.