Question : The area of triangle with vertices A(0, 8), O(0, 0), and B(5, 0) is:
Option 1: 8 sq. units
Option 2: 13 sq. units
Option 3: 20 sq. units
Option 4: 40 sq. units
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Correct Answer: 20 sq. units
Solution :
Let (x
1,
y
1
) = (0, 8)
(x
2,
y
2
) = (0, 0)
(x
3,
y
3
) = (5, 0)
Area of a triangle with vertices (x
1
, y
1
), (x
2
, y
2
), and (x
3
, y
3
)
= $\frac{1}{2}$ [x
1
(y
2
– y
3
) + x
2
(y
3
– y
1
) + x
3
(y
1
– y
2
)]
= $\frac{1}{2}$ [0(0 – 0) + 0(0 – 8) + 5(8 – 0)]
= $\frac{1}{2}$[40]
= 20 sq. units
Hence, the correct answer is 20 sq. units.
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