Question

The three vertices of ∆ABC are A(1, 4), B(−2, 2) and C(3, 2). Plot these points on a graph paper and calculate the area of ∆ABC.

Answer 1

Let A(1,4), B(-2,2) and C(3,2) be the vertices of ∆ABC.
On plotting the points on the graph paper and joining the points, we get ∆ABC as shown above.
Let BC intersect y-axis at D.
Then BC = BD + DC = (2 + 3) units = 5 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 only the magnitude)
Draw AM ⊥​ x -axis meeting BC at L.
Ordinate of point L = ordinate of point C = 2
So, AL = AM - LM = (4 - 2) units = 2 units
∴ Area of (∆ABC) = ½ × BC × AL = ½ × 5 × 2 = 5 sq units