segment KL represents one side of an isosceles right triangle, KLM, with K(2,6), and L(4,2). Triangle KLM is a right angle, and segment KL is congruent to LM.
Since KLM is a right angle, that means that KL and LM are perpendicular. Write and equation in slope-intercept form for KL and then form an equation that is perpendicular to that line.
Using point-slope formula and the slope formula:
(2-6)/(4-2) = -2
That would imply that the slope of the LM is ½. Now you will have to use the distance formula in order to make KL and LM congruent.
Use the distance formula for KL:
√((2-6)^2+(4-2)^2 ) = √20
Now you know that LM also has to have distance of √20.
Use the distance formula again and solve for the unknowns:
√((2-My)^2+(4-Mx)^2 ) = √20 ****
You want to write this in terms of either My or Mx, but you don’t have either right now. Use the fact that L is a point on the line LM and that LM has a slope of ½ to form an equation.
Y-2 = ½(x-4) => y = x/2
Now plug this back into **** and solve for x. You will eventually get something like this:
5x2/4 – 10x = 0
One possible answer to this is (0,0) but that is an extraneous solution since that would mean that LM is not congruent to KL. Solve for
5x/4 – 10 = 0 and you will get your answer is M = (8.4)