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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
6 sq. units
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B
12 sq. units
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C
10 sq. units
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D
20 sq. units
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Solution

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

Area of ΔABC is 12×AB×BC=12×3×4=6 sq.units.

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