If the coordinates of the vertices of A triangle are (0, 0), (0, 2) and (3, 1), `then area of the triangle is

3 sq. units

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-3 sq. units

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2 sq. units

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1 sq. unit

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Solution

The correct option is A 3 sq. units
$L e t t h e t r i a n g l e b e A B C w i t h A = (0, 0), B = (0, 2) a n d C = (3, 1) .$

$∴ T h e v e r t e x A i s$ $a t o r i g i n e . A g a i n t h e$ $o r d i n a t e s o f A & B a r e = 0$
$∴ A B l i e o n t h e Y - a x i s a n d A B = 2 u n i t s .$

$N o w a b s c i s s a o f C = h e i g h t o f t h e Δ [s i n c e A B l i e o n t h e Y - a x i s] .$
$∴ h e i g h t o f t h e Δ = 3 u n i t s$

$∴ a r e a Δ A B C = \frac{1}{2} A B \times h e i g h t = \frac{1}{2} \times 2 \times 3 s q u n i t s = 3 s q u n i t s .$

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