A Plane old problem
Two perpendicular lines in the -plane intersect at . If the sum of their -intercepts is 19, find the sum of the slopes of the two lines.
The answer is -3.5.
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1 solution
Imagine that the point is shifted down such that it is on the x-axis. This question is then equivalent to the following:
Two perpendicular lines in the xy-plane intersect at (2,0). If the sum of their y-intercepts is 7 (because 7=19-6*2), find the sum of the slopes of the two lines.
Now, let the slope of a line be equal to x. We have: 7 = 2x+2/x, or 2x^2-7+2/x=0.
The two roots will represent the two possible slopes, so we want the sum of the two roots, which will always be -b/a (by Vieta’s formulas). This gives us an answer of -7/2.