Question

The quadrilateral with vertices A(-1,-2), B(1,0), C(-1,2) and D(-3,0) is a .

• A. square
• B. rhombus
• C. rectangle

Answer 1

The correct option is A square

Distance between two points with coordinates $(x_1,y_1)$ and $(x_2,y_2)$ = $\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2}$

By applying this formula we get,
AB = $\sqrt{(1+1{)}^2+(0+2{)}^2}=2\sqrt{2}$ units
Similarly we get BC = CD = DA = $2\sqrt{2}$ units
Thus all the sides of the triangle are equal.

AC= $\sqrt{(-1+1{)}^2+(2+2{)}^2}$ =4 units
Similarly we get BD = $\sqrt{(-3-1{)}^2+(0-0{)}^2}$ = 4 units

Thus all the sides are equal and both the diagonals are also equal.
$\therefore$ The quadrilateral formed by the points A(-1,-2), B(1,0), C(-1,2) and D(-3,0) is a square.