Question

point r is located at (3, 2) and point s is located at (8, 15)
what are the coordinates of the point that partitions the directed line segment \\(\overline{rs}\\) in a 1 : 4 ratio?
enter your answer as decimals in the boxes.
(\\(\square\\), \\(\square\\))

Explanation:

Step1: Recall the section formula

The section formula for a point \( P(x,y) \) that divides the line segment joining \( (x_1,y_1) \) and \( (x_2,y_2) \) in the ratio \( m:n \) is \( x=\frac{mx_2 + nx_1}{m + n} \), \( y=\frac{my_2 + ny_1}{m + n} \). Here, \( R(3,2)=(x_1,y_1) \), \( S(8,15)=(x_2,y_2) \), \( m = 1 \), \( n = 4 \).

Step2: Calculate x - coordinate

Substitute values into the x - formula: \( x=\frac{1\times8+4\times3}{1 + 4}=\frac{8 + 12}{5}=\frac{20}{5}=4 \).

Step3: Calculate y - coordinate

Substitute values into the y - formula: \( y=\frac{1\times15+4\times2}{1 + 4}=\frac{15 + 8}{5}=\frac{23}{5}=4.6 \).

Answer:

\((4, 4.6)\)