Question

The line containing the longer diagonal of a quadrilateral whose vertices are A (2, 2), B(-2, -2), C(1, -1), and D(6, 4).

Answer 1

3x -4y = 2

Explanation:

A plot of the points makes it clear that the longest diagonal is BD. The 2-point form of the line through those points can be found by filling in ...

y = (y2 -y1)/(x2 -x1)(x -x1) +y1

y = (4 -(-2))/(6 -(-2))(x -(-2)) +(-2) . . . . . fill in points B and D

y = (6/8)(x +2) -2

4y = 3(x +2) -8 . . . . . . multiply by 4

3x -4y = 2 . . . . . . . . . . add 2-4y