# Thread: slope and line

1. ## slope and line

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

2. Hello

It might be helpful to start by plotting the points and the line you are given.

Can you find the equation of a line from two points? Do you know how to find the gradient of a line perpendicular to another line?

The point C must lie on the line which is perpendicualr to AB and passes through point B (1,6).

Using the points A and B you can find the equation of AB and then BC, see above.

AC is a diagonal of the rectangle and you can find the point C by finding the intersection of the lines AC and BC.

If you plot the co-ordinates of A, B and C you might be able to see how to find the perimeter.

Can you proceed from here. Please ask if you need more help.

3. Originally Posted by kaley015
A rectangle ABCD, where A(3,2) and B(1,6).
(i) Find the equation of BC.
(ii)Given that the equation of AC is y=x-1, Find the coordinates of C.
(iii) the perimeter of the rectangle ABCD. PLEASE HELP!!!
(i)
The equation of BC can be found by the point-slope form of the equation of the line.
(y -y1) = m(x -x1)

You have the point (x1,y1) = B(1,6)
So find the m.
m is the negative reciprocal of the slope of side AB.

You should get the equation of BC as.
(y -6) = (1/2)(x -1)
y = (1/2)x +(11/2) ------------answer.

----------------------
(ii)Given that the equation of AC is y=x-1, Find the coordinates of C.

Get the intersection of
y = (1/2)x +11/2 ----------(1)
and
y = x -1 ------------------(2)
to find the coordinates of point C

You should get C(13,12) ----------answer.

---------------------------------------------
(iii) the perimeter of the rectangle ABCD.

The perimeter of ABCD is twice the sum of AB +BC,
P = 2(AB +CD)

Distance, d, between two points is
d = sqrt[(x2 -x1)^2 +(y2 -y1)^2]

So for AB,
AB = sqrt[(1 -3)^2 +(6 -2)^2] = sqrt(20) = 2sqrt(5)

You should get perimeter of ABCD = 16sqrt(5) ------answer.