Question

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).

Answer 1

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:

$\frac{AP}{PB}=\frac{5}{1}$

AP+PB=AB

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

$x-x_a=5(x_b-x)$

$x-x_a=5x_b-5x$

Adding 5x and subtracting:

$6x=5x_b+x_a$

Dividing by 6:

$\displaystyle x=\frac{5x_b+x_a}{6}$

Substituting:

$\displaystyle x=\frac{5*8+2}{6}=\frac{42}{6}=7$

x=7

Now for the y-axis:

$\displaystyle y=\frac{5y_b+y_a}{6}$

Substituting:

$\displaystyle y=\frac{5*10+4}{6}=\frac{54}{6}=9$

y=9

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