Quadrilateral ABCD has vertices A(-2,1), B(3,3), C(5,7), and D(0,5). Determine whether line AC is perpendicular to line BD.

1 answer

Is line AC perpendicular to line BD

Two lines are perpendicular if their slopes are negative reciprocals of each other (m1 * m2 = -1).

I'll leave the work for finding these lines to you.

AC--through (-2,1), (5,7)
y = 6/7 x + 19/7
slope m1 = 6/7

BD--through (3,3), (0,5)
y = -2/3 x + 5
slope m2 = -2/3

If perpendicular,
m1 * m2 = -1
6/7 * -2/3 = ?

Are the lines perpendicular?
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