Answer:
B(-17,-19)
Explanation:
The coordinates of a point in a segment that goes from A(x1, y1) to C(x2, y2) in a ratio of a to b can be calculated as
[tex]\begin{gathered} \text{ x-coordinate = }\frac{a}{a+b}(x_2-x_1)+x_1 \\ \\ \text{ y-coordinate = }\frac{a}{a+b}(y_2-y_1)+y_1 \end{gathered}[/tex]In this case, A(x1, y1) = (-22, -25) and C(x2, y2) = (3, 5) and the ratio is 1 to 4, so a = 1 and b = 4. Replacing the values, we get:
[tex]\begin{gathered} x-coordinate=\frac{1}{1+4}(3-(-22))-22 \\ \\ x-coordinate=\frac{1}{5}(3+22)-22=\frac{1}{5}(25)-22=5-22=-17 \end{gathered}[/tex][tex]\begin{gathered} y-coordinate=\frac{1}{1+4}(5-(-25))-25 \\ \\ x-coordinate=\frac{1}{5}(5+25)-25=\frac{1}{5}(30)-25=6-25=-19 \end{gathered}[/tex]Therefore, the coordinates of B are (x,y) = (-17,-19)
