Question

The co-ordintates of □KLMN are K(1, 4.5), L(−2, 0), M(1, −4.5) and N(3, 0) respectively. Draw □KLMN and state its type.

Answer 1

We know that distance between the two points (x₁ ,y₁ ) and (x₂ ,y₂ ) is $\sqrt{{\left(y_2-y_1\right)}^2+{\left(x_2-x_1\right)}^2}$.
KL=$\sqrt{{\left(0-4.5\right)}^2+{\left(-2-1\right)}^2}=\sqrt{29.25}$ units
LM= $\sqrt{{\left(-4.5-0\right)}^2+{\left(1+2\right)}^2}=\sqrt{29.25}$ units
MN= $\sqrt{{\left(0+4.5\right)}^2+{\left(3-1\right)}^2}=\sqrt{24.25}$ units
NK=$\sqrt{{\left(4.5-0\right)}^2+{\left(1-3\right)}^2}=\sqrt{24.25}$ units
As KL = LM and MN = NK, the quadrilateral KLMN is a kite.