triangle xyz is reflected over its hypotenuse to create a kite. what is the approximate distance from y to…

Explanation:

Step1: Find the area of triangle XYZ

The area of right - triangle $XYZ$ with legs $a = 5$ and $b = 12$ is $A=\frac{1}{2}\times5\times12 = 30$. Also, the area of triangle $XYZ$ can be expressed as $A=\frac{1}{2}\times$ (hypotenuse) $\times$ (altitude from $Y$ to $XZ$). The hypotenuse $XZ = 13$. Let the altitude from $Y$ to $XZ$ be $h$. Then $30=\frac{1}{2}\times13\times h$, so $h=\frac{60}{13}\approx4.615$.

Step2: Determine the distance from $Y$ to $Y'$

When the triangle is reflected over its hypotenuse, the distance from $Y$ to $Y'$ is twice the length of the altitude from $Y$ to the hypotenuse $XZ$. So the distance from $Y$ to $Y'$ is $d = 2h$. Substituting $h=\frac{60}{13}$, we get $d=\frac{120}{13}\approx9.2$.

Answer:

9.2 units