Explanation:
We need to find the value of k so that the triangle with vertices (1, -1), (-4,2k) and (-k, – 5) is 24 sq. units.
The area of triangle is given by :
![A=(1)/(2)* [x_1(y_2-y_3)-x_2(y_3-y_1)+x_3(y_1-y_2)]](https://img.qammunity.org/2021/formulas/mathematics/high-school/w0ot6gxsx5vh5giimuvy9u8itnw2xcu66r.png)
Here,
x₁ = 1, y₁ = -1, x₂ = -4, y₂ = 2k, x₃ = -k and y₃ = -5
So,
![24=(1)/(2)* [1(2k-(-5))-(-4)((-5)-(-1))+(-k)((-1)-(2k))]](https://img.qammunity.org/2021/formulas/mathematics/high-school/ohv1bw6p43lmuu1axginikc15f0pw1j87u.png)
We need to solve the above equation,
![48=[1(2k-(-5))-(-4)((-5)-(-1))+(-k)((-1)-(2k))]](https://img.qammunity.org/2021/formulas/mathematics/high-school/6qhc6k1vdiuwrbydxyma72dydubdvt1lp7.png)
On solving the above equation we get the value of k as :
k = 4.7