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# Geometry

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In the diagram, $ABCD$ is a square. Find $PR.$

The side length of the square is 10. L, M, N, O are midpoints.

Mar 15, 2024

#1
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Point A is at (0,0), Point B is at (10,0), Point C is at (10,10) Point D is at (0,10).

Then you can draw each of the lines. The equations for each of the lines are: DL: y = -2x + 10, NB: y = -2x + 20, OC: y = 1/2x + 5, and AM: y = 1/2x.

After drawing out all of the lines, you can find that Point R is at (6,8) and point P is at (4,2).

Use the distance formula or pythag to find the length between the two points.

$$\sqrt{2^2+6^2}=\sqrt{40}=2\sqrt10$$

Answer: $$2\sqrt10$$

Mar 15, 2024

#1
+34
+1

Point A is at (0,0), Point B is at (10,0), Point C is at (10,10) Point D is at (0,10).

Then you can draw each of the lines. The equations for each of the lines are: DL: y = -2x + 10, NB: y = -2x + 20, OC: y = 1/2x + 5, and AM: y = 1/2x.

After drawing out all of the lines, you can find that Point R is at (6,8) and point P is at (4,2).

Use the distance formula or pythag to find the length between the two points.

$$\sqrt{2^2+6^2}=\sqrt{40}=2\sqrt10$$

Answer: $$2\sqrt10$$

jilin73 Mar 15, 2024