Question

triangle xyz is reflected over its hypotenuse to create a kite. what is the approximate distance from y to y? round to the nearest tenth. 4.6 units 5.4 units 8.0 units 9.2 units

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, if we consider the hypotenuse $c = 13$ as the base, and let the height (the distance from $Y$ to $XZ$) be $h$. Then $A=\frac{1}{2}\times13\times h$. Since $A = 30$, we have $\frac{1}{2}\times13\times h=30$, so $h=\frac{60}{13}\approx4.615$.

Step2: Use the property of reflection

When $\triangle XYZ$ is reflected over its hypotenuse to create a kite, the distance from $Y$ to $Y'$ is $2h$.
$2h = 2\times\frac{60}{13}=\frac{120}{13}\approx9.2$

Answer:

9.2 units