Question

Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.

In ΔPRQ, the length of is 8 units. The length of mid-segment XY is
units.

Answer 1

From given picture we can see that X is mid point of line PQ

So PQ=2PX

From given picture we can see that Y is mid point of line PR

So PR=2PY

Now consider triangles PRQ and PYX

Sides PQ and PX has same ratio as of sides PR and PY (as calculated above)

angle XPY= angle QPR  (common angle)

Hence triangles PRQ and PYX are similar.

We know that ratio of the sides of similar triangles is always equal so we can write:

$\frac{PQ}{PX} = \frac{QR}{XY}$

Plug the given values QR=8 and PQ=2PX

$\frac{2PX}{PX} = \frac{8}{XY}$

$\frac{2}{1} = \frac{8}{XY}$

$2 = \frac{8}{XY}$

$XY = \frac{8}{2}$

$XY = 4$

Hence final answer is XY = 4 units.

Answer 2

Answer:

4

Step-by-step explanation: