Question

What is the area of rectangle ABCD, if points A, B, C, and D have the following coordinates?

Answer 1

Answer:

The area of the rectangle ABCD is $\frac{2}{5}$ square units.

Step-by-step explanation:

From statement we have that rectangle ABCD is formed by the following points: $A(x,y) = (2, 5), B(x,y) = \left(\frac{8}{3}, 5 \right), C(x,y) = \left(\frac{8}{3}, \frac{28}{5} \right), D(x,y) = \left(2, \frac{28}{5} \right)$. First, we calculate the length of each side by the Pythagorean Theorem:

$AB = \sqrt{\left(\frac{8}{3}-2 \right)^{2}+ (5-5)^{2}}$

$AB = \frac{2}{3}$

$BC = \sqrt{\left(\frac{8}{3}-\frac{8}{3}\right)^{2}+\left(\frac{28}{5}-5\right)^{2} }$

$BC = \frac{3}{5}$

$CD = \sqrt{\left(2-\frac{8}{3} \right)^{2}+\left(\frac{28}{5}-\frac{28}{5} \right)^{2}}$

$CD = \frac{2}{3}$

$DA = \sqrt{\left(2-2\right)^{2}+\left(5-\frac{28}{5} \right)^{2}}$

$BC = \frac{3}{5}$

Which satisfies all minimum characteristics for a rectangle. The area of the rectangle ABCD is the product of its base and its height, that is:

$A = \left(\frac{2}{3}\right)\cdot \left(\frac{3}{5} \right)$

$A = \frac{2}{5}$

The area of the rectangle ABCD is $\frac{2}{5}$ square units.