Question

find the coordinates of the point which divides the line segment joining the point (3,5) and (7,9) in the ratio 2:3 internally

Answer 1

coordinates of point dividing line is (23/5,33/5).

Answer 2

(23/5, 33/5) are the coordinates of the point.

Step-by-step explanation:

Let the given points be A and B,

so,

A =  (3,5)

B = (7,9)

P(x, y) = 2:3

Now, we have

$x_{1} = 3, x_{2} = 7$

$y_{1} = 5, y_{2} = 9$

$m_{1} = 2, m_{2} = 3$

Using internal division, we get

x = $(m_{1} x_{2} + m_{2} x_{1}) / m_{1} + m_{2}$

= {(2)(7) + (3) (3)}/ 2 + 3

= (14 + 9)/5

= 23/5

Now,

y = $(m_{1} y_{2} + m_{2} y_{1}) / m_{1} + m_{2}$

= {(2)(9) + (3) (5)}/ 2 + 3

= (18 + 15)/5

= 33/5

Since x = 23/5 and y = 33/5, the coordinates of the point are (23/5, 33/5)

Learn more: Coordinates of the point

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