Question

The area of the triangle formed by the points $(2,6),(10,0)$ and $(0,k)$ is zero square units. Find the value of $k.$

• A. $\frac{15}{2}$
• B. $\frac{3}{2}$
• C. $\frac{7}{2}$
• D. $\frac{13}{2}$

Answer 1

The correct option is A $\frac{15}{2}$

The area of the triangle is:

$A=\frac{1}{2}\left|y_1\right(x_2-x_3)+y_2(x_3-x_1)+y_3(x_1-x_2\left)\right|$

We are given that the area of the triangle is $0$ and the points are $(2,6)$, $(10,0)$ and $(0,k)$, therefore,

$\Rightarrow 0=\frac{1}{2}\left|6\right(10-0)+0(0-2)+k(2-10\left)\right|\Rightarrow 0=\frac{1}{2}|60-0-8k|\Rightarrow 0=\frac{1}{2}|60-8k|$

$\Rightarrow 60-8k=0\Rightarrow 8k=60\Rightarrow k=\frac{60}{8}=\frac{15}{2}$

Hence, $k=\frac{15}{2}$.