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. A. 4.6 units B. 5.4 units C. 8.0 units…

Question

asked Jul 7, 2019 77.4k views

2 Answers

Alexander Sakhatskii · Answer 1 · 2019-07-14T15:48:25+0000

Answer:

D is correct. 9.2 units is distance from Y to Y'.

Explanation:

Triangle XYZ is reflected over its hypotenuse to create a kite.

Therefore, ΔXYZ and ΔXY'Z would be congruent right angle triangle.

Area of triangle XYZ=
(1)/(2)* XY* YZ

Another formula of area of triangle XYZ if base is XZ

Area of triangle XYZ=
(1)/(2)* XZ* YM

Where, XY=5. YZ=12 and XZ=13

(1)/(2)* YM* 13=(1)/(2)* 5* 12

$YM=(60)/(13)\Rightarrow 4.6\text{ Units}$

Both triangles are congruent. So, YM=Y'M

YY'=YM+MY'

YY'=4.6+4.6

YY'=9.2 Units

Thus, D is correct. 9.2 units is distance from Y to Y'.