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A level Maths help:Coordinate Geometry help

Question 5i) the points A,B, C have coordinate A(2,1), B(b,3) and (5,5), where b>3 and Angle ABC=90, find b

Can someone help me figure out how to get to the answer I have tried so many times and I never reach the correct answer. It will be greatly appreciated

Reply 1

XxKingSniprxX

Take a photo and include it in your thread so its easier for us to help guide and aid you in your work.

bump

Original post by XxKingSniprxX

Take a photo and include it in your thread so its easier for us to help guide and aid you in your work.

Oh, There is no diagram or anything

Reply 4

Meriadoc

Ok, so you need to use the fact that the product of the gradients of AB and CB is -1 because they are perpendicular (as ABC is 90), that is (5-3)/(5-b)*(1-3)/(2-b)=-1, gradients found doing that y1-y2 over x1-x2 thing. From this you can easily get a quadratic in b (multiply everything by
(2-b)/(-2), which is b²-7b+6=0, factorise to (b-6)(b-1)=0 so b=6 because it's greater than 3
I hope this helps you

(edited 9 years ago)

Reply 5

ennahaspatience

Original post by meriadoc

ok, so you need to use the fact that the product of the gradients of ab and cb is -1 because they are perpendicular (as abc is 90), that is (5-3)/(5-b)*(1-3)/(2-b)=-1, gradients found doing that y1-y2 over x1-x2 thing. From this you can easily get a quadratic in b (multiply everything by
(2-b)/(-2), which is b²-7b+6=0, factorise to (b-6)(b-1)=0 so b=6 because it's greater than 3
i hope this helps you