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, ordinate of point B is 1.
AB is parallel to Y-axis, so its abscissa is 1.
Hence, the coordinates of the point B is (1, 1).

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

$\text{Area}\text{of}\Delta ABC\text{is}\frac{1}{2}\times AB\times BC=\frac{1}{2}\times 3\times 4=6\text{sq.units}.$