Question

A quadrilateral has vertices (-5,1) (-2,5) (2,2) (-1,-2). Determine if it is a square by using the distance formula to calculate the length of the diagonals, and the slope formula to determine if the diagonals are perpendicular

Answer 1

Length of diagonals are :

`D_1 = √( (-5-(-1))^2 + (1-(-2))^2 )\\\\D_1 = 5\ units`

`D_2 = √((-2 -2 )^2 + (5-2)^2)\\\\D_2 = 5 \ units`

Now, Slope of both the diagonal is :

`m_1 =(1-(-2))/(-5-(-1)) \\\\m_1 = -(3)/(4)\\\\m_2 = (5-2)/(-2-2)\\\\m_2 = -(3)/(4)`

Now, product of slopes are :

`m_1 * m_2 = (-3)/(4) * (-3)/(4)\\\\m_1 * m_2 = (9)/(16)`

Since, the product of slope is not equal to -1 . It means that the slopes are not perpendicular.

Therefore, this quadrilateral is not square.