Question

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.

Answer 1

Answer: perpendicular

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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

• p = f/e which is the slope of AB
• q = -e/f which is the slope of CD

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.