Question

Cydney is proving that perpendicular lines have slopes that are opposite reciprocals. She draws line p and labels two points on the line as (0, a) and (b, 0). Enter the answers, in simplest form, in the boxes to complete the proof. The slope of line p is . Rotate line p 90° counterclockwise about the origin to get line q. The labeled points on line p map to (−a, 0) and ( , ) on line q. The slope of line q is . The slopes of the lines are opposite reciprocals because the product of the slopes is .

Answer 1

Slope of p = -a/b

(0, b) is on line q

Slope of q = ( b - 0) / (0 - -a) = b/a

Product of the slopes = (-a/b) (b/a) = (-ab) /(ab) = -1

I hope this helps (: Have a whimsical day! lol