Question

Find a point d(x, y) such that the points a(−4, 1), b(3, 0), c(−1, −3), and d are the corners of a square.

Answer 1

- draw the points
- you will see thet AC has the same M as BD
- also AC = BD distance because it is a square
- calculate the M of AC
$\frac{1 - ( - 3)}{ - 4 - ( - 1)} = \frac{4}{ - 3} = - \frac{4}{3} = m$
- calculate AC distance
$\sqrt{ {(1 - ( - 3))}^{2} + {( - 4 - ( - 1))}^{2} } = \\ \sqrt{ {4}^{2} + {( - 3)}^{2} } = \\ \sqrt{25} = 5 = ac$
- lets say d is (x,y)
- now just make to equations with BD distance and M