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

`(1 - ( - 3))/( - 4 - ( - 1)) = (4)/( - 3) = - (4)/(3) = m`
- calculate AC distance

`\sqrt{ {(1 - ( - 3))}^(2) + {( - 4 - ( - 1))}^(2) } = \\ \sqrt{ {4}^(2) + {( - 3)}^(2) } = \\ √(25) = 5 = ac`
- lets say d is (x,y)
- now just make to equations with BD distance and M