Question

In a Cartesian coordinates the vertices of a square are: (1, 1), (0, 8), (4, 5) and (-3, 4) What is the area?

• A. 20 sq. units
• B. 50 sq. units
• C. 25 sq. units
• D. 35 sq. units
• E. none of these

Answer 1

Answer: (B)

50 sq. units

The vertices of a square are $(1,1),(0,8),(4,5)$ and $(-3,4)$

Now,all sides of a square are equal

$\therefore$ distance between the vertices is

$a=\sqrt{(1-0{)}^2+(1-8{)}^2}$

$a=\sqrt{1^2+(-7{)}^2}$

$a=\sqrt{50}$

$a=5\sqrt{2}$

$\therefore$ Area of square=$a^2$

$=(5\sqrt{2}{)}^2$

$=50$ sq. units