SOLUTION: Two points have coordinates A(2,3) and B(6,7).If C(7,t) lies on the perpendicular bisector of AB,find the value of t. Find the coordinates of D such that line AB is the perpendicul

Question 1177471: Two points have coordinates A(2,3) and B(6,7).If C(7,t) lies on the perpendicular bisector of AB,find the value of t. Find the coordinates of D such that line AB is the perpendicular bisector of CD.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
the equation of the line AB:slope is 4/4=1
y-y1=m(x-x1), m slope (x1, y1) point
so y-3=1(x-2)
y=x+1
-
midpoint of AB is half way between x s and half way between y s or (4,5)
so the equation of the line has slope -1 (negative reciprocal of 1 for perpendicular bisector) and the equation is y-5=-1(x-4)
y=-x+9
we are given that C has coordinates (7, t)
so when x=7, y=2
t=2
I am not clear what D is, but C is (7, 2) and the two lines have the equations given above and the graph shows this below.
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