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Question 1127555: The point A has coordinates (-1,5) and the point B has coordinates(7,1) .The perpendicular bisector of AB meets x-axis at C and y-axis at D .Calculate the length of CD.
Answer by greenestamps(13198)   (Show Source):
You can put this solution on YOUR website!
Draw a picture and use it to solve all parts of the problem, instead of using slope formulas and equations of lines. It is easy to see the right numbers in a picture; it is very easy to plug wrong numbers in the wrong places or make calculation errors using formulas and equations.
A(-1,5) and B(7,1) --> midpoint M is (3,3).
From A to B is 8 to the right and down 4, so the slope is -4/8 = -1/2. Then the slope of the perpendicular bisector is the negative reciprocal, 2.
To find the x- and y-intercepts of the perpendicular bisector, again look at the picture. The slope of the perpendicular bisector is 2. To get from the midpoint M to the x-axis you need to go down 3 units; the slope of 2 means you need to move 1.5 to the left.
So the x-intercept is 1.5 units left from 3, at C(1.5,0).
Then from there you need to go another 1.5 units left to get to the y-axis; that means you again need to go down 3 units from 0; so the y-intercept is D(0,-3).
The length of CD is then found using the Pythagorean Theorem. You can do the calculation; the length is 1.5*sqrt(5).
A graph....
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