Question:
The area of the triangle with vertices $(1, 2), (3, 4)$ and $(5, 2)$ is:
The area of the triangle with vertices $(1, 2), (3, 4)$ and $(5, 2)$ is:
Show Hint
If two vertices have the same y-coordinate, the length of that side is the base, and the height is the vertical distance to the third vertex.
Updated On: Apr 8, 2026
- 4
- 8
- 2
- 10
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The Correct Option is A
Solution and Explanation
Step 1: Concept
Area of a triangle with vertices $(x_1, y_1), (x_2, y_2), (x_3, y_3)$ is $\frac{1}{2} |x_1(y_2-y_3) + x_2(y_3-y_1) + x_3(y_1-y_2)|$.
Step 2: Analysis
Area $= \frac{1}{2} |1(4-2) + 3(2-2) + 5(2-4)|$
$= \frac{1}{2} |1(2) + 3(0) + 5(-2)| = \frac{1}{2} |2 - 10|$.
Step 3: Conclusion
Area $= \frac{1}{2} |-8| = 4$.
Final Answer: (A)
Area of a triangle with vertices $(x_1, y_1), (x_2, y_2), (x_3, y_3)$ is $\frac{1}{2} |x_1(y_2-y_3) + x_2(y_3-y_1) + x_3(y_1-y_2)|$.
Step 2: Analysis
Area $= \frac{1}{2} |1(4-2) + 3(2-2) + 5(2-4)|$
$= \frac{1}{2} |1(2) + 3(0) + 5(-2)| = \frac{1}{2} |2 - 10|$.
Step 3: Conclusion
Area $= \frac{1}{2} |-8| = 4$.
Final Answer: (A)
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