Question

In a classroom, 4 friends are seated at the points A, B, C and D as shown in the following figure. The point A(3, 4), B(6, 7), C(9, 4) and D(6, 1) taken in order form the vertices of _________________

• A. Square
• B. Rectangle
• C. Rhombus
• D. Rhombus

Answer 1

The correct option is A Square

Distance between two points $(x_1,y_1)$ and $(x_2,y_2)$

$=\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2}$

$A{B}^2=(6-3{)}^2+(7-4{)}^2$
= 9 + 9
= 18
AB = $\sqrt{18}$ units

$B{C}^2=(9-6{)}^2+(4-7{)}^2$
= 9 + 9
= 18
BC = $\sqrt{18}$ units

$C{D}^2=(6-9{)}^2+(1-4{)}^2$
= 9 + 9
= 18
CD = $\sqrt{18}$ units

$D{A}^2=(3-6{)}^2+(4-1{)}^2$
= 9 + 9
= 18
DA = $\sqrt{18}$ units

Since all the sides are equal, from the given options we can say that the figure is a square