+368 Find the coordinates of the intersection of the diagonals of quadrilateral ABCD, where:
A(3, 6), B(9, 6), C(7, 3), and D(1, 1).
+130042 Slope of diagonal AC = [ 6-3] / [ 3 -7] = -3/4
Equation of line through AC is
y =(-3/4)(x -3) + 6
y = (-3/4)x + 9/4 + 6
y = (-3/4)x + 33/4 (1)
Slope of diagonal BD = [ 6-1] / [ 9-1] = 5/8
Equation of line through BD is
y = (5/8)(x -1) + 1
y = (5/8)x + 3/8 (2)
Set (1) = (2) to find the x intersection pt
(-3/4)x + 33/4 = (5/8)x + 3/8
33/4 - 3/8 = (5/8 + 3/4)x
63/8 = (11/8)x
x = 63/11
y = (5/8) ( 63/11 ) + 3.8
y = 87/22
Intersection pt = ( 63/11, 87/22 )
