SOLUTION: I have two right triangle which are exactly equal and that make a rectangle, if we know three xy coordinates of the the one triangle and all angles how can find unknown xy coordina

Question 280074: I have two right triangle which are exactly equal and that make a rectangle, if we know three xy coordinates of the the one triangle and all angles how can find unknown xy coordinate of the rectangle
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Read everything before you start doing anything

Let

be the right angle vertex of the given triangle. Let

and

be the other two vertices of the given triangle. Finally, let

be the unknown point.

Use the slope formula to calculate the slope of the line containing the segment AB:

Opposite sides of a rectangle are parallel. Parallel lines have equal slopes. Using the point-slope form of the equation of a line write an equation of the line parallel to AB that passes through C.

Call that result Equation 1.

Now repeat the entire process, this time computing the slope of the line containing AC and deriving an equation for its parallel through B.

And call that Equation 2.

Finally, solve the system of equations consisting of Equation 1 and Equation 2. The solution set will be

.

The above is the General solution

If you happen to have a situation where the two legs of your given triangle are parallel to the axes, then the solution is much simpler. Take the

-coordinate of the given point that is on a vertical line above (or below) the unknown point as the

-coordinate of the unknown point. Take the

-coordinate of the given point that is on a horizontal line to the right or left of the unknown point as the

-coordinate of the unknown point. Done.

John

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