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?



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1 answer

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

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