Question

given the points ( g(-1,2) ) and ( h(4,-3) ), determine the coordinates of point ( i ) that divides the directed line segment ( gh ) in the ratio ( 4:1 ).
enter your answer in this format: ( (x,y) ).
use the keypad to enter the answer in the box provided.
the coordinates of point ( i ) is

Explanation:

Step1: Recall the section formula

If a point \(I(x,y)\) divides the line segment joining \(G(x_1,y_1)\) and \(H(x_2,y_2)\) in the ratio \(m:n\), then \(x=\frac{mx_2 + nx_1}{m + n}\) and \(y=\frac{my_2+ny_1}{m + n}\). Here, \(x_1=-1,y_1 = 2,x_2 = 4,y_2=-3,m = 4,n = 1\).

Step2: Calculate the \(x\) - coordinate

Substitute the values into the \(x\) - coordinate formula:
\(x=\frac{4\times4+1\times(-1)}{4 + 1}=\frac{16-1}{5}=\frac{15}{5}=3\)

Step3: Calculate the \(y\) - coordinate

Substitute the values into the \(y\) - coordinate formula:
\(y=\frac{4\times(-3)+1\times2}{4 + 1}=\frac{-12 + 2}{5}=\frac{-10}{5}=-2\)

Answer:

\((3,-2)\)