Question

Indicate the equation of the given line in standard form. 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:

step 1

Plot the figure

we have

A (2, 2), B(-2, -2), C(1, -1), and D(6, 4)

using a graphing tool

The longer diagonal is BD

see the attached figure

step 2

Find the slope of the diagonal BD

we have

B(-2, -2) and D(6, 4)

m=(4+2)/(6+2)

m=3/4

step 3

Find the equation of the diagonal BD into point slope form

y-y1=m(x-x1)

we have

m=3/4

D(6,4)

substitute

y-4=(3/4)(x-6)

step 4

Convert the equation in standard form

The equation of the line in standard form is equal to

Ax+By=C

y-4=(3/4)(x-6)

y=(3/4)x-(18/4)+4

Multiply by 4 both sides

4y=3x-18+16

3x-4y=18-16

3x-4y=2 -----> equation of the diagonal in standard form