+1859 In the diagram, $ABCD$ is a square. Find $PR.$
The side length of the square is 10. L, M, N, O are midpoints.
+129771 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)
