Question

the diagram shows a rectangle ABCD where A is (3,2) and B is (1,6)
(i) Find the equation of BC
Given that the equation of AC is y=x-1 find
(ii) the coordinates of C
(iii) the perimeter of the rectangle ABCD

Answer 1

the line joining B to A is sort of the vector (2,-4). Find the vector orthogonal to this: y=1/2x. You have to add a constant to return it back to its position (before they were all translated down to the origin). Use the fact that BC goes through (1,6) to get y = 1/2x + 11/2. That's the equation of BC.

Now you also have the equation of AC. Where these two lines meet is the point C.

AC = x-1. BC = 1/2x + 11/2
x-1 = 1/2x + 11/2
this gives you x = 13.
Throw that into the equation: c = (13,12)

Calculate some lengths in R2 to get the perimeter.


the line joining B to A is sort of the vector (2,-4). Find the vector orthogonal to this: y=1/2x. You have to add a constant to return it back to its position (before