Question

find the point that divides the directed line segment from (-6, -9) to (-11, -14) in a 4:1 ratio.

Explanation:

Step1: Recall the section formula

The section formula for a point \((x,y)\) that divides the line segment joining \((x_1,y_1)\) and \((x_2,y_2)\) in the ratio \(m:n\) is \(x=\frac{mx_2 + nx_1}{m + n}\) and \(y=\frac{my_2 + ny_1}{m + n}\). Here, \((x_1,y_1)=(-6,-9)\), \((x_2,y_2)=(-11,-14)\), and \(m:n = 4:1\), so \(m = 4\), \(n = 1\).

Step2: Calculate the x - coordinate

Substitute the values into the x - coordinate formula:
\(x=\frac{4\times(-11)+1\times(-6)}{4 + 1}=\frac{-44-6}{5}=\frac{-50}{5}=-10\)

Step3: Calculate the y - coordinate

Substitute the values into the y - coordinate formula:
\(y=\frac{4\times(-14)+1\times(-9)}{4 + 1}=\frac{-56-9}{5}=\frac{-65}{5}=-13\)

Answer:

The point is \((-10,-13)\)