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Question

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


A

10 sq. units

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B

20 sq. units

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C

6 sq. units

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D

12 sq. units

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Solution

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 abscissa since it is parallel to X-axis = 5 - 1 = 4 units
Area of ΔABC is 12×AB×BC=12×3×4 sq.units=6 sq.units.


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