Answer:
(D) x + 10y = 37
Explanation:
The slope of HK is ∆y/∆x = (7 -(-3))/(2 -1) = 10, so the slope of the altitude line will be the negative reciprocal of 10, or -1/10.
This means the line in standard form will have the equation ...
... x + 10y = c . . . . . . . for some value of c
We know the altitude line goes through the opposite vertex (G), so the equation must be satisfied for the coordinates of G.
... (-3) + 10(4) = c = -3 +40 = 37
The equation of the altitude line is ...
... x +10y = 37 . . . . matches selection (D)
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Comment on slope in a standard form equation of a line
In standard form, the equation of a line is ...
... ax + by = c
When solved for y, the equation in slope-intercept form is ...
... y = (-a/b)c + c/b
That is, the slope is -a/b.
We want a line with slope -1/10, so it is convenient to choose a=1, b=10.