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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 points (6,0), (4,3), and (2,1), we can use the formula for the area of a triangle given by the coordinates of its vertices: \[ \text{Area} = \frac{1}{2} \left| x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2) \right| \] Where: - \( (x_1, y_1) = (6, 0) \) - \( (x_2, y_2) = (4, 3) \) - \( (x_3, y_3) = (2, 1) \) ### Step 1: Substitute the coordinates into the formula Substituting the values into the area formula: \[ \text{Area} = \frac{1}{2} \left| 6(3 - 1) + 4(1 - 0) + 2(0 - 3) \right| \] ### Step 2: Simplify the expression inside the absolute value Calculating each term: - \( 6(3 - 1) = 6 \times 2 = 12 \) - \( 4(1 - 0) = 4 \times 1 = 4 \) - \( 2(0 - 3) = 2 \times (-3) = -6 \) Now, substituting these back into the area formula: \[ \text{Area} = \frac{1}{2} \left| 12 + 4 - 6 \right| \] ### Step 3: Combine the terms Now combine the terms inside the absolute value: \[ 12 + 4 - 6 = 10 \] ### Step 4: Calculate the area Now substitute back into the area formula: \[ \text{Area} = \frac{1}{2} \left| 10 \right| = \frac{10}{2} = 5 \] ### Final Result Thus, the area of the triangle is: \[ \text{Area} = 5 \text{ square units} \] ---
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