ABCD is a quadrilateral with angle ABC a right angle. D lies on the perpendicular bisector of AB. The coordinates of A and B are (7, 2) and (2, 5) respectively. The equation of line AD is y=4x-26.
I've already found the equation of the perpendicular bisector of line segment AB, which is y=5/3x-4
a) Find the coordinates of point D.
b) Find the gradient of line BC.
c) Find the value of the second coordinate c of the point C(8, c).
d) Find the area of quadrilateral ABCD.

2. Originally Posted by mandarep
The equation of line AD is y=4x-26.
I've already found the equation of the perpendicular bisector of line segment AB, which is y=5/3x-4
a) Find the coordinates of point D.
The co0rdinates of D will be the intersection of $\displaystyle \displaystyle y=4x-26$ and $\displaystyle \displaystyle y=\frac{5x}{3}-4$ given the 2nd equation is correct. (I have not checked it, )

3. Thanks. I ended up getting D=(66/7, 82/7), which I think is correct.
Do you have any idea how I find the gradient for BC, because I don't have the C coordinates.

4. Originally Posted by mandarep
Do you have any idea how I find the gradient for BC, because I don't have the C coordinates.
You did say this:
"I've already found the equation of the perpendicular bisector of line segment AB, which is y=5/3x-4"
So you know what you're doing...wonder why you're having trouble with this...
BC has same slope as the bisector: 5/3; so using b(2,5): y intercept = 5/3;
now C(8,c): c = (5/3)(8) + 5/3 = 15

5. Sorry. I guess I just didn't realize how straight forward it was.
Thanks for getting me going on the right track.