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.

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Solution

Let A( 2,5), B(-2,2) and C(4,2) be the three vertices of ∆ABC.
On plotting the points on a graph paper and joining the points, we see that points A and C lie in quadrant I and point B lie in quadrant II.
Let BC intersects y-axis at point D.

BC = (BD + DC) = (2 + 4) units = 6 units (Abscissa of B = −2, which indicates that it is on the left side of y-axis. So, for calculating the length of BC, we will consider the magnitude only)
Draw AM ⊥ x-axis and intersect BC at L.
Ordinate of point L = ordinate of point B = ordinate of point C
AL = AM − LM = (5 − 2) units = 3 units
∴ Area of ∆ABC = ½ × BC × AL = ½ × 6 × 3 = 9 sq units

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