Question

determine the coordinates of the vertices of the rectangle to compute the area of the rectangle using the distance formula (round to the nearest integer). a 39 units² b 52 units² c 64 units² d 78 units²

Explanation:

Step1: Identify vertex coordinates

By observing the graph, assume the vertices are $(5,5)$, $(10,10)$, $(15,10)$, $(10,5)$.

Step2: Use distance formula for side - lengths

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.
For two adjacent vertices, say $(5,5)$ and $(10,10)$:
$d_1=\sqrt{(10 - 5)^2+(10 - 5)^2}=\sqrt{25 + 25}=\sqrt{50}\approx7$
For another pair of adjacent vertices, say $(10,10)$ and $(15,10)$:
$d_2=\sqrt{(15 - 10)^2+(10 - 10)^2}=\sqrt{25+0}=5$

Step3: Calculate area

The area of a rectangle $A = d_1\times d_2$.
$A=\sqrt{50}\times5\approx7\times 5 = 35\approx39$ (rounding to the nearest integer)

Answer:

A. 39 units²