Question

what are the coordinates of the point on the directed line segment from (-8,6) to (-3,1) that partitions the segment into a ratio of 2 to 3? answer attempt 1 out of 2

Explanation:

Step1: Recall the section - formula

The formula to find the coordinates of a point \(P(x,y)\) that divides the line - segment joining \(A(x_1,y_1)\) and \(B(x_2,y_2)\) in the ratio \(m:n\) is \(x=\frac{mx_2+nx_1}{m + n}\) and \(y=\frac{my_2+ny_1}{m + n}\). Here, \(x_1=-8,y_1 = 6,x_2=-3,y_2 = 1,m = 2,n = 3\).

Step2: Calculate the x - coordinate

\[

$$\begin{align*} x&=\frac{2\times(-3)+3\times(-8)}{2 + 3}\\ &=\frac{-6-24}{5}\\ &=\frac{-30}{5}\\ &=-6 \end{align*}$$

\]

Step3: Calculate the y - coordinate

\[

$$\begin{align*} y&=\frac{2\times1+3\times6}{2 + 3}\\ &=\frac{2 + 18}{5}\\ &=\frac{20}{5}\\ &=4 \end{align*}$$

\]

Answer:

\((-6,4)\)