Plot the points A(2, 5), B(–2, 2) and C(4, 2) on a graph paper. Join AB, BC and AC. Calculate the area of ∆ABC.
Question:

Plot the points A(2, 5), B(–2, 2) and C(4, 2) on a graph paper. Join AB, BC and AC. Calculate the area of ∆ABC.

Solution:

Abscissa of D = Abscissa of A = 2
Ordinate of D = Ordinate of B = 2

Now,
BC = (2 + 4) units = 6 units
AD = (5 – 2) units = 3 units

Area of $\Delta A B C=\frac{1}{2} \times$ Base $\times$ Height

$=\frac{1}{2} \times B C \times A D$

$=\frac{1}{2} \times 6 \times 3$

$=9$

Hence, area of ∆ABC is 9 square units.