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.

Question

asked Feb 3, 2019 121k views

1 Answer

John Doherty · Answer 1 · 2019-02-08T12:16:54+0000

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:

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

$=√(\left(-1-0\right)^2+\left(-3-\left(-4\right)\right)^2)$

=√(2)

Computing Width :

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

$=√(\left(2-\left(-1\right)\right)^2+\left(0-\left(-3\right)\right)^2)$

=3√(2)

=
$√(2) * 3√(2) = 3 * 2 = 6 \ squares \ units.$ .