The line containing the diagonal of a square whose vertices are A(-3, 3), B(3, 3), C(3, -3), and D(-3, -3). Find two equations, one for each diagonal.

QUESTION POSTED AT 01/06/2020 - 04:20 PM

Answered by admin AT 01/06/2020 - 04:20 PM

Attached to the answer is a graph of the square, based on the points given. From there you can easily guess the equations of the diagonal lines.

However, you do not need a graph in order to solve the problem. 

AC and BD are two pairs of points diagonally across from one another. This is because the pairs do not share the same x or y value. 

Based on the equation of the line:
y = mx+b 
We must find the slope(m) and the y-intercept(b).

Finding slope (m):
Lets use the equation below:
m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}

Line AC:
m =  \frac{-3-3}{3-(-3)}
m =  \frac{-6}{6}
∴ m = -1
 y_{BD} = -1x +b

Line BD:
m = \frac{-3-3}{-3-3}
m = \frac{-6}{-6}
∴ m = 1
∴  y_{BD} = 1x +b

Find y-intercept (b):
In order to find the y-intercept(b) of the line, we must plug in a point that is on that line.

Line AC:
y = -1x + b
3 = -1(-3) + b
3 = 3 + b
b = 0 

Line BD:
y = 1x + b
3 = 1(3) + b
3 = 3 + b
b = 0

Therefore, the equations for the diagonals are as follows:
 y_{AC} = -x
 y_{BD} = x

Hope this helps!
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