I need help on math Hw! Please help me! DESPERATE!?

Question

Let P = (a,b), Q= (0,0), and R= (-b,a), where a and b are positive numbers. Prove that angle PQR is right, by introducing two congruent right triangles into your diagram. Verify the slope of segment QP is the negative reciprocal of the slope of segment QR.
Please Explain and give an exact answer!!


THANK YOU SOO MUCH!!

Answer 1

Here's the sketch:
http://s236.photobucket.com/albums/ff177/jsardi56/?action=view¤t=congruenttriangles10-24-07.jpg

Drop a perpendicular from P to the y axis, meeting the y axis at S.
Drop a perpendicular from R to the y axis meeting the y axis at T.
Measure of SP is a.....[STUDENT FILL IN THE REASONS]
Measure of QT is a
Measure of RT is b
Measure of SQ is b
Angle T and angle S are right angles
Triangle QTP is congruent to triangle RTQ
Angle TQP + angle TPQ = 90 degrees
Angle TQR = angle TPQ
Angle TQP + angle TQR = 90 degrees
Angle PQR is right

Use the slope formula on QP and QR:
QP:
m = (y2 - y1)/(x2 - x1)
m = (b - 0)/(a - 0) = b/a
QR:
m = (y2 - y1)/(x2 - x1)
m = (a - 0)/(-b - 0) = -b/a
The slopes of QP and QR are negative reciprocals of each other, so they are perpendicular.