SOLUTION: ABCD is a rectangle where A is (1,3) and D is (5,5). AC lies on the line 3y=4x+5. find; i) The equation of DC ii) The coordinates of C and B iii) Area of ABCD.

Question 1127764: ABCD is a rectangle where A is (1,3) and D is (5,5). AC lies on the line 3y=4x+5. find;
i) The equation of DC
ii) The coordinates of C and B
iii) Area of ABCD.
Answer by greenestamps(13196) (Show Source): You can put this solution on YOUR website!

I'll try to get you pointed in the right direction and let you do the work....

i) Equation of CD

Since ABCD is a rectangle, you know that CD is perpendicular to AD.
Find the slope of AD using the given coordinates.
The slope of CD is the negative reciprocal of the slope of AD.
Find the equation of CD using the slope of CD and the coordinates of point D.

ii) Coordinates of C and B

C is the intersection of AC and DC. You have the equations for both lines. Solve the pair of equations to find the coordinates of C.
Then find the coordinates of B knowing that opposite sides of the rectangle are parallel and the same length.

(iii) Area of ABCD

The area is length times width. Use the Pythagorean theorem to find the two lengths of the sides of the rectangle.

Hint: If you have done all the calculations correctly, the area is an integer, even though the side lengths are not.
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