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 the line AB is the per

Algebra ->  Coordinate-system -> 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 the line AB is the per      Log On


   

Question 708173: 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 the line AB is the perpendicular bisector of CD.
Answer by josgarithmetic(39838) About Me  (Show Source):
You can put this solution on YOUR website!
Here is help for the first part.

You want the midpoint of segment AB. Determine the slope of line AB using the two given points of A and B. Determine the slope of the line perpendicular to this one; use the fact that m%5B1%5D%2Am%5B2%5D=-1 if line 1 and line 2 are perpendicular.
Whether as general form or standard form, find the equation for this perpendicular line.l Again you need to use the midpoint of AB for this.
Have the equation of this perpendicular line; use C to calculate what t is.

Slope for AB, %287-3%29%2F%286-2%29=1. m=1.
The slope of the perpendicular line is then -1.

Midpoint of AB: (%282%2B6%29%2F2,%283%2B7%29%2F2) = (4,5).

Line 2 which is perpendicular to AB is like y=-1%2Ax%2Bb and MUST contain (4,5).
5=-4+b, so b=9.
Line 2 is then y=-x%2B9.

Line 2 is said t contain point C, (7,t) and we want to find t.
Substitute the point directly into y=-x%2B9.
t=-%287%29%2B9
highlight%28t=2%29