Question

In Fig. 14.46, the area of ΔABC (in square units) is

(a) 15 (b) 10 (c) 7.5 (d) 2.5 [CBSE 2013]

Answer 1

The coordinates of A are (1, 3).

∴ Distance of A from the x-axis, AD = y-coordinate of A = 3 units

The number of units between B and C on the x-axis are 5.

∴ BC = 5 units

Now,

Area of ∆ABC = $\frac{1}{2}\times \mathrm{BC}\times \mathrm{AD}=\frac{1}{2}\times 5\times 3=\frac{15}{2}=7.5$ square units

Thus, the area of ∆ABC is 7.5 square units.

Hence, the correct answer is option C.