Final answer:
To find the ratio in which P(4,5) divides the line joining the points A(2,3) and B(7,8), calculate the distances between P and A and between P and B. The ratio is 2:3.
Step-by-step explanation:
To find the ratio in which P(4,5) divides the line joining the points A(2,3) and B(7,8), we need to calculate the distances between P and A and between P and B.
Distance between P and A = √((4-2)^2 + (5-3)^2) = √(2^2 + 2^2) = √8
Distance between P and B = √((4-7)^2 + (5-8)^2) = √((-3)^2 + (-3)^2) = √18
The ratio in which P divides the line AB is the ratio of the distances between P and A and between P and B. Therefore, the ratio is √8 : √18, which can be simplified to 2√2 : 3√2. Thus, the ratio is 2:3.