Correct answers only . you will be reported ! indicate the equation of the given line in standard form. show all of your work for full credit. 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).

PQ = sqrt((-1-3)^2 + (1-5)^2) = sqrt(16 + 16) = sqrt(32)
PR = sqrt((-1-5)^2 + (1 + 5)^2) = sqrt(36 + 36) = sqrt(72)
QR = sqrt((3-5)^2 + (5+5)^2) = sqrt(4 + 100) = sqrt(104)

Since QR is the longest side, QR must be the hypotenuse.

slope = m = (y2 - y1)/(x2 - x1)

The slope of QR is m = (-5 - 5)/(5 - 3) = -10/2 = -5

The slope of the perpendicular to QR is 1/5.

The altitude to QR passes through P(-1, 1) and has slope 1/5.

y - y1 = m(x - x1)

y - 1 = 1/5(x - (-1))

y - 1 = 1/5(x + 1)

5y - 5 = x + 1

x - 5y = -6    Answer