Question

The line containing the altitude to the hypotenuse of a right triangle whose vertices are P(-1, 1), Q(3, 5), and R(5, -5). Is what?

Answer 1

Having drawn the points I can discern that the right angle is at P and the hypotenuse is QR. The slope of QR is (-5 - 5)/(5 - 3) = -10 / 2 = -5. Then the slope of the altitude must be the negative inverse of this, or 1/5. Then we need the line that passes through QPR with this slope. We can construct this from the point-slope form.

y - 1 = ( x + 1 ) / 5 or
\[y = \frac{ x }{ 5 } + \frac{ 6 }{ 5 }\]