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.

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:

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

Hence final answer is XY = 4 units.

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