Question

P(1,Y) is a point on AB. (0,2) and (3,5) are the coordinates of A and B respectively. Find the ratio AP/PB and the value of y.

Answer 1

use formula ,
$\bf{(x,y)=\{\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n}\}}$

Let P divides the line joining points A and B is m : n ratio .
so, $\bf{x=\frac{mx_2+nx_1}{m+n}}$
1 = (m × 3 + n × 0)/(m + n)
1 = (3m + 0)/(m + n)
1 × (m + n) = 3m
m + n = 3m
n = 2m
m/n = 1/2
hence, P divides the line joining points A and B is 1 : 2 ratio.
therefore, AP/PB = 1/2

now, y = (1 × 5 + 2 × 2)/(1 + 2)
y = (5 + 4)/3 = 3

Answer 2

Answer:

I think you can find a better answer in the textbook only

Step-by-step explanation: