# Math Help - AS Level Maths question.

1. ## AS Level Maths question.

Question:
A(7,2) and C(1,4) are two vertices of a square ABCD.
a) Find in the form ax +by=c the equation of the diagonal BD.
b) Find the coordinates of B and of D.

I have done part a) and got the answer 3x-y=9
but i don't know how to do part b)
thanks x

2. Originally Posted by caramel17
Question:
A(7,2) and C(1,4) are two vertices of a square ABCD.
a) Find in the form ax +by=c the equation of the diagonal BD.
b) Find the coordinates of B and of D.

I have done part a) and got the answer 3x-y=9
but i don't know how to do part b)
thanks x

Hi Caramel17,

You know the midpoint of AC is (4, 3). Let's call that point M.

You found the slope of the perpendicular which passes through
points B and D.

That would be 3.

Using the slope of 3 and the midpoint M(4, 3) and an endpoint B(x, y), we get:

$\dfrac{3-y}{4-x}=\dfrac{3}{1}$

Equating the numerators and denominators, we arrive at:

$4-x=1 \: \text{and} \:3-y=3$

$x=3 \:\:\text{and}\:\:y=0$

$\boxed{B(x, y) = B(3, 0)}$

You can find the coordinates of D in a similar fashion.

Let coordinates of D be $(x_1, y_1)$

$\dfrac{y_1-3}{x_1-4}=\dfrac{3}{1}$

$x_1-4=1 \: \text{and}\:y_1-3=3$

$x_1=5 \:\text{and}\:y_1=6$

$\boxed{D(x_1, y_1) = D(5,6)}$