Question

Find the coordinates of the point which divides the line segment joining the points (6,3) and (-4,5) in the ratio 3:2 internally

Answer 1

by section formula we get
(x, y) = (3*-4+2*6)/5 , (3*5+2*3)/5
= (0,21/5)
hence this is the required answer

Answer 2

Answer:

(0, 21/5)

Step-by-step explanation:

Given:- Co-ordinates of end points of a line segment are (6, 3) and (-4, 5).

To find:- Co-ordinates of the point that divides the line segment joining the points (6,3) and (-4,5) in the ratio 3:2 internally.

Solution:-

The Section formula states that if a point (x, y) divides a line segment joining the points ($x_{1}$, $y_{1}$) and ($x_{2}$, $y_{2}$) internally in the ratio m:n, then

                           (x, y) = $(\frac{mx_{2}+nx_{1} }{m+n}, \frac{my_{2} +ny_{1} }{m+n} )$ ------- ( 1 )

Now substituting the values of ($x_{1}$, $y_{1}$) = (6, 3) and ($x_{2}$, $y_{2}$) = (-4, 5) and m = 3 and n = 2 in the above equation, we get

⇒ x = $\frac{3*(-4)+2*6}{3+2}$              and          ⇒ y = $\frac{3*5+2*3}{3+2}$

⇒ x = (-12 + 12) ÷ 5         and          ⇒ y = (15 + 6) ÷ 5

⇒ x = 0 ÷ 5                     and          ⇒ y = 21 ÷ 5

⇒ x = 0                           and         ⇒ y = 21/5

Therefore, (0, 21/5) divides the line segment joining the points (6, 3) and (-4, 5) in the ratio 3:2 internally.

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