Answer:
0
Explanation:
Consider the diagram below:
Point P divides segment CD in the ratio 3:2.
To find the coordinate of P, we use the formula for the internal division of a line segment given below:
[tex]P(x,y)=\mleft(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\mright)[/tex]
Thus, the x-coordinate of P is:
[tex]\begin{gathered} \dfrac{mx_2+nx_1}{m+n}=\frac{3(4)+2(-6)}{3+2}\text{ where }\begin{cases}m\colon n=3\colon2 \\ x_1=-6,x_2=4\end{cases} \\ =\frac{12-12}{5} \\ =\frac{0}{5} \\ =0 \end{gathered}[/tex]
The x-coordinate of P is 0.
Extra
The y-coordinate of P is:
[tex]\begin{gathered} \dfrac{my_2_{}+ny_1}{m+n}=\frac{3(5)+2(0)}{3+2}\text{ where }\begin{cases}m\colon n=3\colon2 \\ y_1=0,y_2=5\end{cases} \\ =\frac{15+0}{5} \\ =\frac{15}{5} \\ =3 \end{gathered}[/tex]
The y-coordinate of P is 3.
