Question

Two vertices of a right triangle have the coordinates (−2, 5) and (9, 5) .

What is the length of the side formed by these vertices?



Enter your answer in the box.

units

Answer 1

To find the length of the side formed by the vertices \((-2, 5)\) and \((9, 5)\), we can calculate the distance between these two points. Since both points have the same y-coordinate, the distance is simply the difference in their x-coordinates.

The formula for the distance between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

In this case:

- \(x_1 = -2\)
- \(y_1 = 5\)
- \(x_2 = 9\)
- \(y_2 = 5\)

Calculating the distance:

\[
d = \sqrt{(9 - (-2))^2 + (5 - 5)^2}
\]
\[
= \sqrt{(9 + 2)^2 + 0^2}
\]
\[
= \sqrt{11^2}
\]
\[
= \sqrt{121}
\]
\[
= 11
\]

Thus, the length of the side formed by these vertices is

\[
\boxed{11} \text{ units}
\]