Find point P that divides segment AB into 2 3 ratio The point should be closer to AA -3 1 and B 3 5?

Answer 1

To find point P that divides segment AB in the ratio 2:3, we can use the section formula. Let A be (-3, 1) and B be (3, 5). The coordinates of point P can be calculated using the formula:

[ P = \left( \frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n} \right) ]

where (m=2), (n=3), (x_1=-3), (y_1=1), (x_2=3), and (y_2=5). Plugging in the values, we get:

[ P = \left( \frac{2 \cdot 3 + 3 \cdot (-3)}{2+3}, \frac{2 \cdot 5 + 3 \cdot 1}{2+3} \right) = \left( \frac{6 - 9}{5}, \frac{10 + 3}{5} \right) = \left( -\frac{3}{5}, \frac{13}{5} \right) ]

Thus, point P is located at ((-0.6, 2.6)).