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# Geometry/find point

Question
Hi Wilson,

I explain more about previous question, so if we have known 3 points ABC, AB is a line, A(-2,2), B(2,-2), and for example point C(1,2). can you help me step by step to find point D that line CD is a perpendicular to line AB.

thanks

Fendi

To be perpendicular to AB, we need the slope m from A to B.
The slope of the perpendicular line would be -1/m.

The slope from A to B is (yB-yA)/(xB-xA) = -4/4 = -1 = m.
This makes -1/m = 1.

The line through C with slope 1 is y-2 = x-1, and this can be rewritten as y = x+1.

The line containing A and B is y-2 = -1(x+2) => y = -x.

Setting these two equal gives where they cross.
That is, x+1 = -x.  Adding x-1 to both sides gives 2x = -1, which means x = -1/2.

Using either line, we can see that y = 1/2.

Geometry

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#### Scott A Wilson

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