Question

now, answer the question
find the coordinates of point ( d ) along the directed line segment ( er ) with endpoints ( e(4,-2) ) and ( r(-3,1) ) so that the ratio of ( overline{ed} ) and ( overline{dr} ) is ( 2:3 ). use the keypad to enter the answer in the box provided. express your answer in the format ( left(\frac{x}{a},\frac{y}{b}
ight) ), with fractions in simplest form.
the coordinates of point ( d ) are

Explanation:

Step1: Use the section formula

If a point \(D(x,y)\) divides the line segment joining \(E(x_1,y_1)\) and \(R(x_2,y_2)\) in the ratio \(m:n\), then the coordinates of \(D\) are given by \(x=\frac{mx_2 + nx_1}{m + n}\) and \(y=\frac{my_2+ny_1}{m + n}\). Here, \(x_1 = 4,y_1=-2,x_2=-3,y_2 = 1,m = 2,n = 3\).

Step2: Calculate the \(x\) - coordinate

Substitute the values into the \(x\) - coordinate formula:
\(x=\frac{2\times(-3)+3\times4}{2 + 3}=\frac{-6 + 12}{5}=\frac{6}{5}\)

Step3: Calculate the \(y\) - coordinate

Substitute the values into the \(y\) - coordinate formula:
\(y=\frac{2\times1+3\times(-2)}{2+3}=\frac{2-6}{5}=\frac{-4}{5}\)

Answer:

\((\frac{6}{5},-\frac{4}{5})\)