If , , and are the vertices of a right triangle with right angle , find the value of .
The value of for the right triangle at with vertices , , and .
To check the triangle to be right triangle, we need to prove that any two lines are perpendicular to each other.
If two lines are perpendicular, then the product of their slopes is or one slope is negative reciprocal of the other slope.
(i.e) If , then or
The slope of the line that contains the points and is given by
Let , , and be vertices of the right triangle.
The right angle is given at .
Thus the line and are perpendicular to each other.
By finding the slopes of these lines, we can easily determine the value of .
Let , and are the slopes of the line and respectively.
The given points are and .
Using the slope formula and choosing , , , and
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