Coordinates Of A Point In Space

The coordinates of point P dividing the line joining points

A(x_1%2C%20y_1)

and

B(x_2%2C%20y_2)

in the ratio

m%3An

are given by the section formula:

P%5Cleft(%5Cfrac%7Bm%20x_2%20%2B%20n%20x_1%7D%7Bm%20%2B%20n%7D%2C%20%5Cfrac%7Bm%20y_2%20%2B%20n%20y_1%7D%7Bm%20%2B%20n%7D%5Cright)

Here,

A(2%2C%203)

B(10%2C%207)

, and the ratio is

3%3A1

. Substitute the values into the section formula:

P%5Cleft(%5Cfrac%7B3%20%5Ctimes%2010%20%2B%201%20%5Ctimes%202%7D%7B3%20%2B%201%7D%2C%20%5Cfrac%7B3%20%5Ctimes%207%20%2B%201%20%5Ctimes%203%7D%7B3%20%2B%201%7D%5Cright)

P%5Cleft(%5Cfrac%7B30%20%2B%202%7D%7B4%7D%2C%20%5Cfrac%7B21%20%2B%203%7D%7B4%7D%5Cright)%20%3D%20P%5Cleft(%5Cfrac%7B32%7D%7B4%7D%2C%20%5Cfrac%7B24%7D%7B4%7D%5Cright)

P(8%2C%206)

Final answer
Answer:

%5Cboxed%7B(8%2C%206)%7D

Chapter Questions
1 MCQs