Will a triangle with vertices at points A (0; 0) B (3; 1) C (1; 7) be rectangular?

We have the vertices of the triangle: A (0; 0), B (3; 1), C (1; 7).

Let’s find the lengths of the sides of the triangle using the formula for finding the distance between two points with known coordinates:

AB = ((3 – 0) ^ 2 + (1 – 0) ^ 2) ^ (1/2) = 10 ^ (1/2);

AC = ((1 – 0) ^ 2 + (7 – 0) ^ 2) ^ (1/2) = 50 ^ (1/2);

BC = ((1 – 3) ^ 2 + (7 – 1) ^ 2) ^ (1/2) = (4 + 36) ^ (1/2) = 40 ^ (1/2).

Found the lengths of the triangle. Let’s check the action of the Pythagorean theorem:

50 = 10 + 40.

The square of one side is equal to the sum of the squares of the other two sides.

The triangle is rectangular.