Soltuion
Step 1:
A(6, 5) and B(6, 15)
Step 2
Write the formula for the division of line segment into ratio a:b
[tex]\begin{gathered} Coordinates\text{ of a point that divide a line segemnt into ratio a:b} \\ =\text{ \lparen}\frac{bx_1+ax_2}{a+b}\text{ , }\frac{by_1+ay_2}{a+b}\text{ \rparen} \end{gathered}[/tex]Step 3:
Substitute into the formula to find the coordinates:
a = 3, b = 2
[tex]\begin{gathered} x_1\text{ = 6, y}_1\text{ = 5, x}_2\text{ = 6, y}_2\text{ = 15} \\ \\ =\text{ \lparen }\frac{2\times6+3\times6}{3+2}\text{ , }\frac{2\times5\text{ + 3}\times15}{3+2}) \\ \\ =\text{ \lparen}\frac{12+18}{5}\text{ , }\frac{10\text{ + 45}}{5}\text{ \rparen} \\ \\ =\text{ \lparen }\frac{30}{5}\text{ , }\frac{55}{5}\text{ \rparen} \\ \\ =\text{ \lparen 6 , 11\rparen} \end{gathered}[/tex]Final answer
( 6 , 11 )
