Question

point g (□, □) is \\(\frac{2}{5}\\) the distance from j to k. write your answer in decimal form. j(-7,2) k(8,-3)

Explanation:

Step1: Recall the section formula

The coordinates of a point \( G(x,y) \) that divides the line segment joining \( J(x_1,y_1) \) and \( K(x_2,y_2) \) in the ratio \( m:n \) are given by \( x=\frac{mx_2 + nx_1}{m + n} \) and \( y=\frac{my_2 + ny_1}{m + n} \). Here, \( m = 2 \), \( n=5 - 2=3 \) (since \( G \) is \( \frac{2}{5} \) from \( J \) to \( K \), so the ratio \( m:n = 2:3 \)), \( x_1=-7 \), \( y_1 = 2 \), \( x_2 = 8 \), \( y_2=-3 \).

Step2: Calculate the x - coordinate of G

Substitute the values into the x - coordinate formula:
\( x=\frac{2\times8+3\times(-7)}{2 + 3}=\frac{16-21}{5}=\frac{-5}{5}=-1.0 \)

Step3: Calculate the y - coordinate of G

Substitute the values into the y - coordinate formula:
\( y=\frac{2\times(-3)+3\times2}{2 + 3}=\frac{-6 + 6}{5}=\frac{0}{5}=0.0 \)

Answer:

\( G(-1.0, 0.0) \)