Question

Dejah is proving that perpendicular lines have slopes that are opposite reciprocals. She draws line s and labels two points on the line as (−a, 0) and (0, b).

Enter the answers, in simplest form, in the boxes to complete the proof.

Answer 1

• b/a; (b, 0); -a/b; -1

Explanation:

Given:

Slope of Line S - (b - 0)/(0 - (-a)) = b/a

Remember the clockwise rule:

(-a, 0) → (0, a)

(0, b) → (b, 0)

Slope of line T - (0- a)/(b - 0) = -a/b = -a/b

The product of slopes: b/a × (-a/b) = -1

So, finally, our answer is:

• b/a; (b, 0); -a/b; -1

Carry On Learning!

Answer 2

• b/a; (b, 0); -a/b; -1

Explanation:

Slope of line s:

• (b - 0)/(0 - (-a)) = b/a

Rotation 90 clockwise rule:

• (-a, 0) → (0, a)
• (0, b) → (b, 0)

The slope of line t:

• (0- a)/(b - 0) = -a/b = -a/b

The product of slopes:

• b/a*(-a/b) = -1