ANSWER:
10.2 units
STEP-BY-STEP EXPLANATION:
The first thing is to make a sketch of the triangle formed in the Cartesian plane, like this:
The hypotenuse is the side opposite the right angle, therefore, it would be the side from the point (-6, 5) to the point (4, 3).
We calculate the distance between these two points using the following formula:
[tex]d=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}[/tex]
We replace and calculate the length of the hypotenuse:
[tex]\begin{gathered} d=\sqrt{\left(4-\left(-6\right)\right)^2+\left(3-5\right)^2} \\ d=\sqrt[]{(4+6)^2+(3-5)^2} \\ d=\sqrt[]{(10)^2+(-2)^2} \\ d=\sqrt[]{100+4} \\ d=\sqrt[]{104} \\ d\cong10.2 \end{gathered}[/tex]
The length of the hypotenuse is 10.2 units.
