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Let $ABCD$ be a trapezoid with bases $\overline{AB}$ and $\overline{CD}.$ Let $AD=5$ and $BC=7,$ and let $P$ be a point on side $\overline{CD}$ such that $\frac{CP}{PD}=\frac{7}{5}.$ Let $X,Y$ be the feet of the altitudes from $P$ to $\overline{AD},$ $\overline{BC}$ respectively. Show that $PX=PY.$

 Jun 19, 2020
 #1
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Please fix your latex and I will give you a hint on your writing problem.

 Jun 19, 2020
 #2
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Let ABCD be a trapezoid with bases AB and CD. Let AD=5 and BC=7, and let P be a point on side CD such that CP/PD=7/5. Let X and Y be the feet of altitudes from P to AD and BC respectively. Show that PX=PY

Guest Jun 19, 2020
 #3
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Think about the area for a triangle.

 

What is the formula?

 

This is not the official way to do it but this is the way I did it and it is correct.

hugomimihu  Jun 19, 2020
 #4
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I used triangles to find the ratio of the areas.

Guest Jun 19, 2020
 #5
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Yes, can you figure something out from that?

hugomimihu  Jun 19, 2020
 #6
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im not sure plz help

Guest Jun 19, 2020
 #7
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write out the formula for the triangles.

 

Then observe the PY and PX.

hugomimihu  Jun 19, 2020

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