CAT 2022 Slot 2 · Quant · Coordinate Geometry · easy

Units) of the triangle with vertices (1,2), (4,6) and (6,2).

Single correct option

Find the area (in sq. units) of the triangle with vertices (1,2), (4,6) and (6,2).

A. 8
B. 9
C. 10
D. 12

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Answer: (C) 10

Area = ½|x₁(y₂−y₃)+x₂(y₃−y₁)+x₃(y₁−y₂)| = ½|1(6−2)+4(2−2)+6(2−6)| = ½|4+0−24| = ½×20 = 10 sq. units. Alternatively, the base along y=2 runs from (1,2) to (6,2), length 5, and the height (vertical distance to (4,6)) is 4, giving area = ½×5×4 = 10.

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