Question

Find the area of the triangle with vertices A(5,4), B(-2,4) and C(2,14).

• A. 34 sq. units
• B. 35 sq. units
• C. 36 sq. units
• D. 32 sq. units

Hint:

Since A and B have the same y-coordinate (4), the base is horizontal with length $|5 - (-2)| = 7$ and height is $|14 - 4| = 10$. Area = $\frac{1}{2} \times 7 \times 10 = 35$.

Answer 1

The Correct Option is B

Step 1: Concept
The 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: Meaning
Plug in the coordinates: $x_1=5, y_1=4; x_2=-2, y_2=4; x_3=2, y_3=14$.

Step 3: Analysis
Area = $\frac{1}{2} |5(4 - 14) + (-2)(14 - 4) + 2(4 - 4)|$ = $\frac{1}{2} |5(-10) + (-2)(10) + 0|$ = $\frac{1}{2} |-50 - 20|$ = $\frac{1}{2} |-70|$.

Step 4: Conclusion
Area = 35 sq. units. Final Answer: (B)