Can someone me answer this 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). the slope of line s is rotate line s 90° clockwise about the origin to get line t. the labeled points on line s map to (0, a) and on line t. the slope of line t is the slopes of the lines are opposite reciprocals because the product of the slopes is i know the first answer is b/a. is the second point for line t (b, 0) or (-b, 0)? i'm not sure what that one is.

first blank: b/a

second blank: (b, 0)

third blank: -a/b

fourth blank : -1  

Step-by-step explanation:

To calculate the slope you need two points as coordinates (x,y). Points on line s: (-a, 0) and (0, b).  The formula is:

slope: (y2 - y1)/(x2 - x1) = (b - 0)/(0 - (-a)) = b/a

Rotation 90° clockwise translate point (x, y) -> (y, -x). Then, (-a, 0) -> (0, a) and (0, b) -> (b, 0)

The points on line t are: (b, 0) and (0, a).  Then, the slope is

slope: (y2 - y1)/(x2 - x1) = (a - 0)/(0 - b) = -a/b

The product of the slopes is: (b/a)*(-a/b) = -1, therefore, the lines are opposite reciprocals.

beanburito

step-by-step explanation: