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Circles and gradients

http://www.thomas-reddington.com/uploads/7/7/8/3/778329/c2_qp_jan_2009.pdf

For question 5a)

In the mark scheme they are finding the gradeints for PQ and QR, then multiplying them, I have no idea why?
Reply 1
Avatar for Joshmeid
Joshmeid
5
Find the gradient of PQ, find the perpendicular for the gradient of QR, find the equation of QR, substitute the y value for a.

You should be familiar with m1m2 = -1, another way of finding the perpendicular gradient.
(edited 12 years ago)
Reply 2
Avatar for Coulson72
Coulson72
theyre perpandicular (because the triangle inside a semicircle is right angled) and hence the product of their gradients is -1.
So from this it should be easy to work out your value for a :smile:
Reply 3
Avatar for zoxe
zoxe
OP
7
Original post by Joshmeid
Find the gradient of PQ, find the perpendicular for the gradient of QR, find the equation of QR, substitute the y value for a.

You should be familiar with m1m2 = -1, another way of finding the perpendicular gradient.


This is the first time i've seen of m1m2 = -1.
Reply 4
Avatar for Joshmeid
Joshmeid
5
Original post by zoxe
This is the first time i've seen of m1m2 = -1.


m1 is the gradient of PQ.

Lets say PQ = 5 for example.

we have m1m2 = -1

We now substitute m1 = 5

5m2 = -1

m2 = -1/5
Reply 5
Avatar for zoxe
zoxe
OP
7
ive solved it with Pythagoras, however i'm still baffled on how theyve done it
Reply 6
Avatar for zoxe
zoxe
OP
7
Original post by Joshmeid
m1 is the gradient of PQ.

Lets say PQ = 5 for example.

we have m1m2 = -1

We now substitute m1 = 5

5m2 = -1

m2 = -1/5


Why does PQ = gradient?

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