Question

Determine whether the quadrilateral is a parallelogramQ(-10,-2) R(1,-1) S(1,-7) T(-11,-8) (Use distance formula)

Answer 1

Parallelograms

The distance between two points (x1,y1) and (x2,y2) is calculated by:

$d=\sqrt[]{(x2-x1)^2+(y2-y1)^2}$

To find if the quadrilateral QRST is a parallelogram, we calculate the distances QR and ST because they are opposite sides. If they are equal, then we calculate the distances RS and TQ.

If both pairs of distances are equal, then our shape is a parallelogram.

Calculate dQR:

$dQR=\sqrt[]{(1+10)^2+(-1+2)^2}=\sqrt[]{11^2+1^2}=\sqrt[]{122}$

Calculate dST:

$dST=\sqrt[]{(-11-1)^2+(-8+7)^2}=\sqrt[]{12^2+1^2}=\sqrt[]{145}$

The opposite sides of the quadrilateral have different lengths, so this is not a parallelogram