Question

each side of a square is 4 cm long. one vertex of the square is at (3,2) on a square coordinate grid marked in centimeter units. which of the following points on the grid could be another vertex of the square?
a. (7,2)
b. (3,4)
c. (1,0)
d. (1,-2)
e. (-2,4)

Explanation:

Step1: Calculate the distance between \((3,2)\) and each option

Use the distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\) for two points \((x_1,y_1)\) and \((x_2,y_2)\).
For option A: \((x_1 = 3,y_1 = 2)\), \((x_2=7,y_2 = 2)\)
\(d=\sqrt{(7 - 3)^2+(2 - 2)^2}=\sqrt{4^2+0^2}=\sqrt{16}=4\)
For option B: \((x_1 = 3,y_1 = 2)\), \((x_2 = 3,y_2 = 4)\)
\(d=\sqrt{(3 - 3)^2+(4 - 2)^2}=\sqrt{0^2+2^2}=\sqrt{4}=2\)
For option C: \((x_1 = 3,y_1 = 2)\), \((x_2 = 1,y_2 = 0)\)
\(d=\sqrt{(1 - 3)^2+(0 - 2)^2}=\sqrt{(-2)^2+(-2)^2}=\sqrt{4 + 4}=\sqrt{8}=2\sqrt{2}\)
For option D: \((x_1 = 3,y_1 = 2)\), \((x_2 = 1,y_2=-2)\)
\(d=\sqrt{(1 - 3)^2+(-2 - 2)^2}=\sqrt{(-2)^2+(-4)^2}=\sqrt{4+16}=\sqrt{20}=2\sqrt{5}\)
For option E: \((x_1 = 3,y_1 = 2)\), \((x_2=-2,y_2 = 4)\)
\(d=\sqrt{(-2 - 3)^2+(4 - 2)^2}=\sqrt{(-5)^2+2^2}=\sqrt{25 + 4}=\sqrt{29}\)

Answer:

A. \((7,2)\)