Question

If the vertices of triangle are (-2,6), (3,-6) and (1,5), then the area of the triangle is

• A. 40 sq. units
• B. 30 sq. units
• C. 15.5 sq. units
• D. 35 sq. units

Answer 1

The Correct Option is C

Let's label the vertices of the triangle as \(A(-2,6), B(3,-6), and\ C(1,5).\)
The formula to calculate the area of a triangle formed by three points \(A(x_1, y_1), B(x_2, y_2), and\  C(x_3, y_3)\) is:
\(\text{Area} = \frac{1}{2} \left| x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2) \right|\)
Substituting the coordinates of the vertices into the formula:
\(\text{Area} = \frac{1}{2} \left| -2(-6 - 5) + 3(5 - (-6)) + 1(6 - (-6)) \right|\)
 \(=\frac{1}{2} \left| -2(-11) + 3(-1) + 1(12) \right|\)
\(=\) \(\frac{1}{2} \times (22 - 3 + 12)\)
= \(\frac{1}{2} \times 31\)
= \(\frac{31}{2}\)
= 15.5
Therefore, the area of the triangle is 15.5 square units (option C).