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avatar+1479 

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

 

 

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

 Dec 18, 2023
 #1
avatar+126665 
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Let A =  (0,0)

Let D = (0,10)

Let C= (10,10)

Let B = (10,0)

 

Line through DL  has the equation y = (-2)x + 10

Line through AM has the equation y=  (1/2)x

x intersection of these lines

-2x + 10 = 1/2x

-(5/2)x = -10

x = 4       

y=  2 

P = (4,2)

 

Line through OC has the equation  y = (1/2)x + 5

Line through NV has the equation  y = (-2)(x -10)  = -2x + 20

x intersection of these lines

(-2x) + 20 = (-1/2)x + 5

(-5/2)x = -15

x = 6

y = 8

R = (6,8)

 

 PR =  sqrt [ (4 - 6)^2 + (2 - 8)^2 ] = sqrt [  4 + 36 ] =  sqrt 40 =   2sqrt (10)

 

cool cool cool

 Dec 19, 2023

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