Question

1. find the perimeter of the square abcd: image of coordinate grid with points a(1, 4), b(-3, 1), d(4, 0), c(0, -3)

options:
a. 5
b. 25
c. 20
d. 16

1. find the area of the square abcd: image of coordinate grid with points a(1, 4), b(-3, 1), d(4, 0)

Explanation:

Question 7:

Step1: Calculate side length using distance formula

The distance formula between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\). Let's find the length of side \(AB\) with \(A(1, 4)\) and \(B(-3, 1)\).
\[

$$\begin{align*} AB&=\sqrt{(-3 - 1)^2 + (1 - 4)^2}\\ &=\sqrt{(-4)^2 + (-3)^2}\\ &=\sqrt{16 + 9}\\ &=\sqrt{25}\\ & = 5 \end{align*}$$

\]

Step2: Calculate perimeter of square

The perimeter \(P\) of a square is \(P = 4\times \text{side length}\). Since side length is \(5\),
\[
P = 4\times5 = 20
\]

Step1: Determine side length (from Question 7)

From Question 7, we found the side length of square \(ABCD\) is \(5\) (using distance formula on \(AB\)).

Step2: Calculate area of square

The area \(A\) of a square is \(A=\text{side length}^2\). So,
\[
A = 5^2=25
\]

Answer:

C. 20

Question 8: