Choose the correct answer from the given four options in the following questions: The area of a triangle with vertices A (3, 0), B (7, 0) and C (8, 4) is (A) 14 (B) 28 (C) 8 (D) 6

Home » Choose the correct answer from the given four options in the following questions: The area of a triangle with vertices A (3, 0), B (7, 0) and C (8, 4) is (A) 14 (B) 28 (C) 8 (D) 6

Choose the correct answer from the given four options in the following questions: The area of a triangle with vertices A (3, 0), B (7, 0) and C (8, 4) is (A) 14 (B) 28 (C) 8 (D) 6

Solution:

Option (C) 8 is the correct answer.

The vertices of the triangle are,

$A\text{ }({{x}_{1}},\text{ }{{y}_{1}})=\left( 3,\text{ }0 \right)$

$B\text{ }({{x}_{2}},\text{ }{{y}_{2}})=\left( 7,\text{ }0 \right)$

$C\text{ }({{x}_{3}},\text{ }{{y}_{3}})=\left( 8,\text{ }4 \right)$

Area of triangle $=\frac{1}{2}[{{x}_{1}}\left( {{y}_{2}}-{{y}_{3}} \right)+{{x}_{2}}({{y}_{3}}-{{y}_{1}})+{{x}_{3}}\left( {{y}_{1}}-{{y}_{2}} \right)]$

$=\frac{1}{2}\left[ 3(0-4)+7\left( 4-0 \right)+8\left( 0-0 \right) \right]$

$=\frac{1}{2}\left[ -12+28+0 \right]$

$=\frac{1}{2}\left[ 16 \right]$

$=8$

As a result, the area of ΔABC is 8.

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