Plot the points A(2,1), B(-1, 2), C(-2, -1) and D(1, -2) in the coordinate plane. Is ABCD Class 9

Plot the points A(2,1), B(-1, 2), C(-2, -1) and D(1, -2) in the coordinate plane. Is ABCD Class 9

Question 1.

Plot the points A(2,1), B(-1, 2), C(-2, -1) and D(1, -2) in the coordinate plane. Is ABCD a square? Can you explain why? What is the area of this square?

Solution:

$\begin{aligned} \mathrm{AB} & =\sqrt{(-1-2)^2+(2-1)^2} \\ & =\sqrt{9+1} \\ & =\sqrt{10} \text { units } \\ \mathrm{BC} & =\sqrt{(-2+1)^2+(-1-2)^2} \\ & =\sqrt{10} \text { units } \\ \mathrm{CD} & =\sqrt{(1+2)^2+(-2+1)^2} \\ & =\sqrt{10} \text { units } \\ \mathrm{AD} & =\sqrt{(1-2)^2+(-2-1)^2} \\ & =\sqrt{10} \text { units } \\ \mathrm{AC} & =\sqrt{(-2-2)^2+(-1-1)^2} \\ & =\sqrt{20} \text { units } \\ \mathrm{BD} & =\sqrt{(1+1)^2+(-2-2)^2} \\ & =\sqrt{20} \text { units }\end{aligned}$

∴ ABCD is a square ........ [sides are congruent and diagonals are congruent]

Area of square = side²

$=(\sqrt{10})^2$

= 10 sq. units