We can tell that the consecutive sides are perpendicular, as their slopes are opposite reciprocals.
1 ( - 1 ) = -1
Therefore, our parallelogram is a rectangle. To check if it is a rhombus and square, we can find the lengths of its sides using the Distance Formula.
Distance Formula: sqrt((x_2-x_1)^2+(y_2-y_1)^2)
Side
Endpoints
Substitute
Simplify
QR
Q( 12,0) and R( 6,- 6)
sqrt(( 6- 12)^2+( - 6- 0)^2)
6sqrt(2)
RS
R( 6,- 6) and S( 0, 0)
sqrt(( 0- 6)^2+( 0-( - 6))^2)
6sqrt(2)
ST
S( 0, 0) and T( 6, 6)
sqrt(( 6- 0)^2+( 6- 0)^2)
6sqrt(2)
TQ
T( 6,6) and Q( 12,0)
sqrt(( 12- 6)^2 + ( 0- 6)^2)
6sqrt(2)
Our parallelogram has four congruent sides. Therefore, it is a rhombus, a rectangle and a square.
