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Question 85380: Please help me
Given points A(10,4) and B(6,-12), show that P(4,-3) is on the perpendicular bisector of line AB
Answer by vertciel(183)   (Show Source):
You can put this solution on YOUR website! Hello there,
The perpendicular bisector meets the straight line at the midpoint of the line. The midpoint of this intersection would be (8,-4) since A and B are (10,4) and (6, -12) respectively.
To show that P(4,-3) is on the perpendicular bisector, you can substitute the values of P into the equation of the perp. bisector. Of course, you would need to find this equation first.
1) Find the slope of the line AB. Denote
2) Denote the midpoint of line AB as M or anything else you like.
3) Now that you know the slope of AB, what would be the slope of MP?
4) y - y1 = m(x - x1): Write the equation for MP. You know that MP passes through (8, -4)
5) Plug the values of P into the equation.
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