Question

What is the area of a rectangle with vertices at ​ (0, −4) ​, ​ (−1, −3) ​ , (2, 0) , and (3, −1) ? Enter your answer in the box.

Answer 1

We are given vertices of a rectangle (0, −4) ​, ​ (−1, −3) ​ , (2, 0) , and (3, −1).

Length is the distance between (0, −4) ​and ​ (−1, −3) points.

Width is distance between  (−1, −3) ​ and (2, 0) points.

Computing length:

$\mathrm{Compute\:the\:distance\:between\:}\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad \sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}$

$=\sqrt{\left(-1-0\right)^2+\left(-3-\left(-4\right)\right)^2}$

$=\sqrt{2}$

Computing Width :

$\mathrm{The\:distance\:between\:}\left(-1,\:-3\right)\mathrm{\:and\:}\left(2,\:0\right)\mathrm{\:is\:}$

$=\sqrt{\left(2-\left(-1\right)\right)^2+\left(0-\left(-3\right)\right)^2}$

$=3\sqrt{2}$

Area of the rectangle = Length × Width  

= $\sqrt{2} \times 3\sqrt{2} = 3 \times 2 = 6 \ squares \ units.$.