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 the 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

Since BC is parallel to X-axis, the ordinate of point B is 1.
AB is parallel to Y-axis, so its abscissa is 1.
The point B is (1,1).

Length of AB is the difference of ordinates since it is parallel to Y-axis = 4 - 1 = 3 units.
Length of BC is the difference of abscissae since it is parallel to X-axis = 5 - 1 = 4 units.

$\Delta ABCis\frac{1}{2}\times AB\times BC=\frac{1}{2}\times 3\times 4sq.units=6sq.units.$