Answer:
y = 1/2x -1
Step-by-step explanation:
The slope of AB is ...
(y2 -y1)/(x2 -x1) = (1 -7)/(4 -1) = -6/3 = -2
Segment BC will be perpendicular to AB, so will have a slope that is the negative reciprocal of this:
slope of BC = -1/(-2) = 1/2
The line containing BC must go through point B, so we can use a point-slope form of the equation for a line:
y = m(x -h) +k . . . . for a line with slope m through point (h, k)
Point B is (4, 1) and our slope is 1/2, so the line's equation can be written ...
y = (1/2)(x -4) +1
y = 1/2x -2 +1 . . . . eliminate parentheses
y = 1/2x -1 . . . . . . . collect terms. This is the equation.
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The attachment shows segment AB and a perpendicular line through B. You will note that it has y-intercept -1 and slope 1/2, as above.
