First, we need to think about this geometric situation. Point A is at the origin. Point B is somewhere on the y-axis, so AB is a vertical line in the xy-plane. If angle ABC = 90°, the only way a line can be perpendicular to a vertical line is by being horizontal. Segment BC must be horizontal.
If BC is horizontal, this means that point B and point C must have the same y-coordinate, because any two points on the same horizontal line in the coordinate plane have the same y-coordinate. This fact allows us to set up an equation.
4a – 5 = 2a + 6
2a = 11
We can leave this in terms of 2a, because all the expression have either 2a or 4a in them. Thus, we know
Even a rough sketch would be enough: we know that leg AB = 17 and leg BC = 12, and these can be consider the base and the height. (It actually doesn't matter which we call the base and which we call the height.)
Answer = (A)
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