Question

Indicate the equation of the given line in standard form, writing the answer in the equation box below.

The line containing the longer diagonal of a quadrilateral whose vertices are A(2, 2), B(-2,-2), C(1, -1), and D16, 4).

Answer 1

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Answer:

x -3y = 4

Explanation:

A plot of the points reveals the longer diagonal to be BD. (Also, point C is on that line.)

We can write the standard form equation of the line through (x1, y1) and (x2, y2) as ...

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

For points (-2, -2) and (16, 4), this equation is ...

(4 -(-2))x -(16 -(-2))y = (4 -(-2))(-2) -(16 -(-2))(-2)

6x -18y = -12 +36

Dividing by the greatest common factor (6), we have the standard-form equation ...

x -3y = 4