The vertices J(2,6), K(7,8), L(9,3), and M(?, ?) determine a square. Show your work to find the coordinates of M. Use complete sentences and proper grammar to give a justification why JKLM is a square.
let the fourth vertex be M(x,y)
slope KJ = slope LM
2/5 = (y-3)/(x-9)
2x - 18 = 5y - 15
2x - 5y = 3 #1
slope JP = slope LM
(y-6)/(x-2) = -5/2
2y - 12 = -5x + 10
5x + 2y = 22 #2
#1 times 2 ---> 4x - 10y = 6
#2 times 5 ---> 25x + 10y = 110
add them:
29x = 116
x = 4
back into #2
20 + 2y = 22
y = 1
M is (4,1)
check my arithmetic