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If (6,0),(4,3),(2,1) is the vertices of ...

If (6,0),(4,3),(2,1) is the vertices of a triangle then the area of the triangle is:

A

3 square unit

B

4 square unit

C

5 square unit

D

6 square unit

Text Solution

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The correct Answer is:
To find the area of the triangle with vertices at the points (6,0), (4,3), and (2,1), we can use the formula for the area of a triangle given its vertices \((x_1, y_1)\), \((x_2, y_2)\), and \((x_3, y_3)\): \[ \text{Area} = \frac{1}{2} \left| x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2) \right| \] ### Step-by-step Solution: 1. **Identify the coordinates**: - Let \((x_1, y_1) = (6, 0)\) - Let \((x_2, y_2) = (4, 3)\) - Let \((x_3, y_3) = (2, 1)\) 2. **Substitute the coordinates into the area formula**: \[ \text{Area} = \frac{1}{2} \left| 6(3 - 1) + 4(1 - 0) + 2(0 - 3) \right| \] 3. **Calculate each term**: - First term: \(6(3 - 1) = 6 \times 2 = 12\) - Second term: \(4(1 - 0) = 4 \times 1 = 4\) - Third term: \(2(0 - 3) = 2 \times (-3) = -6\) 4. **Combine the terms**: \[ \text{Area} = \frac{1}{2} \left| 12 + 4 - 6 \right| = \frac{1}{2} \left| 10 \right| = \frac{10}{2} = 5 \] 5. **Final result**: The area of the triangle is \(5\) square units.
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