Given the points A(0, 0), B(e, f), C(0, e) and D(f, 0), determine if line segments AB and CD are parallel, perpendicular or neither.

Question

asked May 4, 2021 60.0k views

1 Answer

Xi · Answer 1 · 2021-05-08T01:30:28+0000

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Work Shown:

Use the slope formula to find the slope of line AB

m = (y2-y1)/(x2-x1)

m = (f-0)/(e-0)

m = f/e

Let p = f/e so we can compare the slope later

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Use the slope formula to find the slope of line CD

m = (y2-y1)/(x2-x1)

m = (0-e)/(f-0)

m = -e/f

Let q = -e/f so we can compare the slope later

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We have

Multiply the values of p and q

p*q = (f/e)*(-e/f) = (f(-e))/(ef) = (-ef)/(ef) = -1

since p*q = -1, this means the lines AB and CD are perpendicular. They form a 90 degree angle.