Question

The area (in sq units) of the triangle formed by the points $(2,2)$, $(5,5)$ and $(6,7)$is

• A. $\frac{9}{2}$
• B. $5$
• C. $10$
• D. $\frac{3}{2}$
• E. $14$

Answer 1

The correct option is D

$\frac{3}{2}$

Explanation for correct answer:

Determining the area of the traingle:

Given three points of a triangle are $(2,2)$, $(5,5)$ and $(6,7)$.

Now let us suppose ,

$(x_1,y_1)=\left(2,2\right)$

$(x_2,y_2)=\left(5,5\right)$

$(x_3,y_3)=\left(6,7\right)$

We know that the area of a triangle, with coordinates is given as:

$$\begin{gathered} Area=\frac{1}{2}\left\{x_1\left(y_2-y_3\right)+x_2\left(y_3-y_1\right)+x_3\left(y_1-y_2\right)\right\} \\ =\frac{1}{2}\left\{2\left(5-7\right)+5\left(7-2\right)+6\left(2-5\right)\right\} \\ =\frac{1}{2}\left\{2\times \left(-2\right)+5\times 5+6\times \left(-3\right)\right\} \\ =\frac{1}{2}\left\{-4+25-18\right\} \\ =\frac{3}{2} \end{gathered}$$

Therefore the area of the triangle is equal to $\frac{3}{2}\text{square}\text{units}$

Hence, the correct answer is option (D).