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.
[2 Marks]

Answer 1

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). [0.5 Marks]

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 abscissas since it is parallel to X-axis = 5 - 1 = 4 units. [0.5 Marks]

$\therefore Ar\left(\Delta ABC\right)=\frac{1}{2}\times AB\times BC=\frac{1}{2}\times 3\times 4sq.units=6sq.units.$ [1 Mark]