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 35 units²
b 50 units²
c 60 units²

Explanation:

Step1: Find the coordinates of vertices

Let the vertices be \(A(5,10)\), \(B(10,5)\), \(C(15,10)\) (assuming the rectangle - based on the graph structure).

Step2: Calculate the length of one side

Using the distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\) for \(A(5,10)\) and \(B(10,5)\):

$$
LATEXBLOCK0
$$

For \(B(10,5)\) and \(C(15,10)\):

$$
LATEXBLOCK1
$$

(Another approach: Notice that the base length (horizontal distance from \(x = 5\) to \(x=15\)) is \(10\) units and the height (vertical distance from \(y = 5\) to \(y = 10\)) is \(5\) units.

Step3: Calculate the area of the rectangle

The area of a rectangle \(A=\text{length}\times\text{width}\). Here, length \(l = 10\) (horizontal span) and width \(w=5\) (vertical span). So \(A=10\times5 = 50\)

Answer:

B. \(50\) units\(^{2}\)