Question

the endpoints of the directed segment bt are b(-8, 15) and t(4,-9). what are the coordinates of point s such that it partitions the line segment bt in a ratio 1:3? (-4,4) (-5,9) (0,-12) (-4,6)

Explanation:

Step1: Recall the section - formula

If a point \(S(x,y)\) divides the line - segment joining \(B(x_1,y_1)\) and \(T(x_2,y_2)\) in the ratio \(m:n\), then \(x=\frac{mx_2+nx_1}{m + n}\) and \(y=\frac{my_2+ny_1}{m + n}\). Here, \(x_1=-8,y_1 = 15,x_2 = 4,y_2=-9,m = 1,n = 3\).

Step2: Calculate the \(x\) - coordinate of \(S\)

\[

$$\begin{align*} x&=\frac{1\times4+3\times(-8)}{1 + 3}\\ &=\frac{4-24}{4}\\ &=\frac{-20}{4}\\ &=-5 \end{align*}$$

\]

Step3: Calculate the \(y\) - coordinate of \(S\)

\[

$$\begin{align*} y&=\frac{1\times(-9)+3\times15}{1 + 3}\\ &=\frac{-9 + 45}{4}\\ &=\frac{36}{4}\\ &=9 \end{align*}$$

\]

Answer:

\((-5,9)\)