# Math Help - abcd

1. ## abcd

a (7,2) and c (1,4) are two vertices of a square abcd

find in form ax + by = c the equation of the diagonal bd

thanks

2. First, find all the vertices.
A(7,2)
B(7,4)
C(1,4)
D(1,2)
The diagonal |BD| has slope Dy/Dx.
m = Dy/Dx = (2-4)/(1-7) = 1/3
General line formula:
y = mx + C
y = 1/3x + C
We know that the line will pass through B(7,4) and D(1,2).
y = 1/3x + C
4 = 1/3 7 + C
C = 5/3
So the equation becomes,
y = 1/3x + 5/3
3y = x + 5
-x + 3y = 5

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Edit: Aaaah the question was about a square, I thought it was a rectangle :S

I don't have time to solve it at the moment, I think I can help you later..

3. Hello, gracey!

The center of the square is the midpoint of $AC\!:\;O(4,3)$

The slope of $AC$ is: . $m_1 \:=\:\frac{2-4}{7-1}\:=\:-\frac{1}{3}$

Since the diagonals of a square are perpendicular,
. . the slope of $BD$ is: . $m_2 \:=\:+3$

Now write the equation of the line through $(4,3)$ with slope 3.