Answer:
Point P has coordinates (7,9) (last choice)
Step-by-step explanation:
We are given the endpoints A(2,4) B(8,10) and the point P lying on the segment AB with the condition that P partitions it in the ratio 5:1.
This means the distances AP, PB and AB follow the conditions:
[tex]\frac{AP}{PB}=\frac{5}{1}[/tex]
AP+PB=AB
We can work with each coordinate separately. Suppose P has coordinates (x,y), thus:
[tex]x-x_a=5(x_b-x)[/tex]
[tex]x-x_a=5x_b-5x[/tex]
Adding 5x and subtracting:
[tex]6x=5x_b+x_a[/tex]
Dividing by 6:
[tex]\displaystyle x=\frac{5x_b+x_a}{6}[/tex]
Substituting:
[tex]\displaystyle x=\frac{5*8+2}{6}=\frac{42}{6}=7[/tex]
x=7
Now for the y-axis:
[tex]\displaystyle y=\frac{5y_b+y_a}{6}[/tex]
Substituting:
[tex]\displaystyle y=\frac{5*10+4}{6}=\frac{54}{6}=9[/tex]
y=9
Point P has coordinates (7,9) (last choice)
