Find the coordinates of P so that P partitions segment A to B in the ratio 5:1 with A(2, 4) and B(8, 10).

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:

AP+PB=AB

We can work with each coordinate separately. Suppose P has coordinates (x,y), thus:

Adding 5x and subtracting:

Dividing by 6:

Substituting:

x=7

Now for the y-axis:

Substituting:

y=9

Point P has coordinates (7,9) (last choice)

you can first factor out the n to get n(1+5). we know that 1+5 is 6, so we just have 6n.