Find the coordinates of the point that divides the line segment between points Q(2, 3) and R(8, 7) in the ratio 1:3.

To find the coordinates of the point that divides the line segment between points \( Q(2, 3) \) and \( R(8, 7) \) in the ratio \( 1:3 \), we can use the section formula. The section formula states that if a point \( P \) divides the line segment joining points \( A(x_1, y_1) \) and \( B(x_2, y_2) \) in the ratio \( m:n \), then the coordinates of point \( P \) are given by: \[ P\left( \frac{mx_2 + nx_1}{m+n}, \frac{my_2 + ny_1}{m+n} \right) \] In this case, we have: - \( A = Q(2, 3) \) with coordinates \( (x_1, y_1) = (2, 3) \) - \( B = R(8, 7) \) with coordinates \( (x_2, y_2) = (8, 7) \) - The ratio \( m:n = 1:3 \) (where \( m = 1 \) and \( n = 3 \)) Now, we can substitute these values into the section formula: 1. Calculate the x-coordinate of point \( P \): \[ x = \frac{1 \cdot 8 + 3 \cdot 2}{1 + 3} = \frac{8 + 6}{4} = \frac{14}{4} = 3.5 \] 2. Calculate the y-coordinate of point \( P \): \[ y = \frac{1 \cdot 7 + 3 \cdot 3}{1 + 3} = \frac{7 + 9}{4} = \frac{16}{4} = 4 \] Thus, the coordinates of the point that divides the line segment between points \( Q(2, 3) \) and \( R(8, 7) \) in the ratio \( 1:3 \) are: \[ \boxed{(3.5, 4)} \]