A rhombus ABCD has opposite vertices at A(-3,2) and C(9,-2). Find the equations of its diagonals. One of the other vertices is B(4,3).

Find the fourth vertex D
Equation of AC
Equation of BD
Coordinates of D

1 answer

the slope of AC is -1/3

Thus the line AC is

y-2 = -1/3 (x+3)

The diagonals are perpendicular bisectors. The midpoint of AC is (3,0). The slope of BD is 3, so the line BD is

y-0 = 3(x-3)

Note that you don't need the other vertices B and D.