Question

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

• A. 12 sq.units
• B. 10 sq.units
• C. 6 sq.units
• D. 4 sq.units

Answer 1

The correct option is C

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.
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 abscissae since it is parallel to $x$-axis = 5 - 1 = 4 units
$\Delta ABCis\frac{1}{2}\times AB\times BC=\frac{1}{2}\times 3\times 4sq.units=6sq.units.$