Question

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).

Answer 1

x -5y = -6

Explanation:

A plot of the given points shows the hypotenuse is QR, and the vertex through which the altitude line goes is point P. We want a line through P that is perpendicular to QR.

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form of the equation

The equation for a line perpendicular to the one through (x1, y1) and (x2, y2) can be written in the general form ...

(x2 -x1)(x -h) +(y2 -y1)(y -k) = 0

where (x, y) = (h, k) is a point on the line.

values filled in

Using points Q(3, 5) and R(5, -5) for the two points, and (h, k) = P(-1, 1), we have ...

(5 -3)(x -(-1)) +(-5-5)(y -1) = 0

2x +2 -10y +10 = 0 . . . . . . . . . eliminate parentheses

The standard-form equation will have mutually-prime coefficients and the constant on the right. Dividing by 2 and subtracting 6 gives ...

x -5y = -6