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 be

Answer 1

@TheSmartOne

Answer 2

Well, the slope of line p would be a/b, since the y variable increases from 0 to a as the x variable increases from 0 to b.
If you do the rotation as described, line q would have the point (0, b) on the y axis. And the slope of line q would be -b/a, by the same reasoning we used to find the slope of line p.

Answer 3

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

Answer 4

@SmokeyBrown u agree ?

Answer 5

hmm convincing enough

Answer 6

Yeah, cupcake is right, I was wrong about the slopes

Answer 7

nah both of you were good

Answer 8

thx a lot man

Answer 9

best responds ?

Answer 10

yup