SOLUTION: The end points of AB are (2,3) and (8,1) the perpendicular bisector of AB is CD and point C lies on AB the length of CD is the square root of 10

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Question 975942: The end points of AB are (2,3) and (8,1) the perpendicular bisector of AB is CD and point C lies on AB the length of CD is the square root of 10
Answer by Boreal(15235) About Me  (Show Source):
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This is correct.
The distance between the two points is the square root of the difference of the x s ^2 plus the square root of the difference of the ys ^2. The distance is square root of (40)= which is 2 square root of 10. Half the distance is the square root of 10. square root of 40=square root of (4*10).
The equation of the line through the points has slope -2/6 or -1/3
y-y1=(-1/3)((x-x1)
y-3= (-1/3) (x-2)
y= -(1/3)x +(2/3)+3 = -(1/3)x+11/3
perpendicular line has slope 3 (negative reciprocal)
goes through midpoint which is half the distance between the two points (5,2)
Its equation is y-2=3(x-5)
y=3x-13
graph%28300%2C200%2C-20%2C20%2C-20%2C20%2C%28-x%2F3%29%2B%2811%2F3%29%2C+3x-13%29