Question

there is a coordinate plane with a blue square (or rhombus) with vertices a(7, 9) and b(10, 5) marked. below the graph, there are multiple - choice options:
a) 20 m; 25 m²
b) 21.5 m; 29 m²
c) 22.3 m; 31 m²
d) 25 m; 25 m²

Explanation:

Step1: Calculate the side length using the distance formula

The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). For points \(A(7,9)\) and \(B(10,5)\), \(x_1 = 7,y_1=9,x_2 = 10,y_2 = 5\). Then \(d=\sqrt{(10 - 7)^2+(5 - 9)^2}=\sqrt{3^2+(- 4)^2}=\sqrt{9 + 16}=\sqrt{25}=5\).

Step2: Calculate the perimeter of the square

Since it is a square (all sides are equal), the perimeter \(P = 4s\) (where \(s\) is the side - length). With \(s = 5\), \(P=4\times5 = 20\).

Step3: Calculate the area of the square

The area of a square \(A=s^2\). With \(s = 5\), \(A = 5^2=25\).

Answer:

A. \(20\space m;25\space m^{2}\)