| 11. The segment between (0,2) and (2,0) has a slope of -1. You can verify this by finding (y2-y1)/(x2-x1) = (0-2)/(2-0) = (-2)/2 = -1
Two lines are perpendicular if their slopes are negative reciprocals of eachother. Since AB has slope -1, line L bust have slope -(1)/(-1) = 1
It bisects AB, so it must go through the midpoint of it, by definition. So we find the midpoint of AB by this formula: (((x1 +X2)/2),((y1+y2)/2))
So we get ((0+2)/2), (2+0)/2) = (1,1)
So we need a line with slope 1 passing through (1,1). This is obviously the equation y = x, which passes though (0,0)
If you didn't catch that, you could do it the long way:
Slope 1, so y = 1x + b
Plug in point (1,1) to get y-intercept
1 = 1 + b
b=0
OK, now we look for what point would go on the line y = x, which is easy because the x and y have to be the same. Therefore the answer is (3,3), or D. |