Question

1. find the area of the square abcd:

a(1, 4), b(-3, 1), c(0, -3), d(4, 0)
options:
a. 5
b. 25
c. 20
d. 16

Explanation:

Step1: Calculate the length of side AB

Using the distance formula $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$ for points A(1, 4) and B(-3, 1):
$d_{AB} = \sqrt{(-3 - 1)^2 + (1 - 4)^2} = \sqrt{(-4)^2 + (-3)^2} = \sqrt{16 + 9} = \sqrt{25} = 5$

Step2: Calculate the area of the square

The area of a square is side length squared. Since the side length (AB) is 5, the area is $5^2 = 25$.

Answer:

B. 25