Question

Plot A(0, 2), B(2, 3), C(4, 2) and D(2, -4) on a graph paper. Classify the quadrilateral ABCD. Find its area.

Answer 1

Here is the plot of the quadrilateral formed by points A(0, 2), B(2, 3), C(4, 2), and O(2, -4).

Classification of Quadrilateral ABCD

AC is horizontal: A(0,2) to C(4,2) → length = 4

BD is vertical: B(2,3) to D(2,−4) → length = 7

Both diagonals intersect at right angles (at the centre (2,2)), and the figure is symmetric.

ABCD is a kite, since:

Adjacent sides are equal in pairs

Diagonals intersect at 90°

Area of Quadrilateral ABCD

Area = `1/2 xx d_1 xx d_1`

Diagonal 1 (AC) = 4 units

Diagonal 2 (BD) = 7 units

Area = `1/2 xx 4 xx 7`

Area = 14

Quadrilateral ABCD is a kite.

Area = 14 square units.