Question

If the adjacent vertices of a square are (2, 5) and (6, 8), the area of the square is square units.

• A. 16
• B. 25
• C. 30

Answer 1

The correct option is B 25

Given: Adjacente vertices of square are (2, 5) and (6, 8).

The distance between two points $(x_1,y_1)\text{and}(x_2,y_2)$ is $\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2}.$

So, the side of the square = $\sqrt{(6-2{)}^2+(8-5{)}^2}$

The side of the square = $\sqrt{(4{)}^2+(3{)}^2}$

The side of the square = $\sqrt{16+9}$

The side of the square = $\sqrt{25}$

​​​​​​​​​​​​​​The side of the square = 5 units

Area of the square = (side)${}^2$

Area of the square = (5)${}^2$ = 25 square units