Question

The area of the triangle with vertices $(1, 2), (3, 4)$ and $(5, 2)$ is:

• A. 4
• B. 8
• C. 2
• D. 10

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.

Answer 1

The Correct Option is A

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)