Question

A right triangle is formed by the points A(2, -1), B(2, 5), and C(6, -1). Find the length of the hypotenuse, which is the line segment BC.

1) 10
2) 20
3) 8
4) 13
5) ���74

Answer 1

The length of the hypotenuse BC of the right triangle is 4 units.

Step-by-step explanation:

The length of the hypotenuse of the right triangle can be found using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

So, for the given triangle with vertices A(2, -1), B(2, 5), and C(6, -1), we can calculate the length of the hypotenuse BC.

Using the distance formula, the length of BC is:

d = sqrt((6 - 2)²+ (-1 - (-1))²) = sqrt(4² + 0²) = sqrt(16) = 4

Therefore, the length of the hypotenuse BC is 4 units.