Question

A right triangle is formed by connecting the 3 coordinates A, B and C. Find the area of the $\Delta ABC$, if AB and BC are parallel to the coordinate axes as shown in figure.

• A. 6 sq. units
• B. 12 sq. units
• C. 10 sq. units
• D. 20 sq. units

Answer 1

The correct option is A

6 sq. units

The point B lies on both the lines AB and BC. Hence it satisfies the properties of both AB and BC.
Since BC is parallel to X-axis, so y-coordinate of C is equal to y-coordinate of B.

$\therefore$ y-coordinate of B = 1
and AB is parallel to Y-axis, so x-coordinate of A is equal to x-coordinate of B.

$\therefore$ x-coordinate of B = 1

$\therefore$ point B is (1,1).

Length of AB is difference of their y-coordinates since it is parallel to Y-axis = 4 - 1 = 3 units
Length of BC is difference of their x-coordinates since it is parallel to X-axis = 5 - 1 = 4 units
$Areaof\Delta ABCis\frac{1}{2}\times AB\times BC=\frac{1}{2}\times 3\times 4sq.units=6sq.units.$