Question

find the coordinates of point which divides the join of the line segment of the pionts (-3,5)and (2,-5)in the ratio 2:3​

Answer 1

Explanation:

ANSWER

Let the points be A(5,−2) and B(9,6). Let a point P(x,y) divides AB in the ratio 3:1.

Using section formula, we have

P(x,y)=(  

3+1

3×9+1×5

​  

,  

3+1

3×6+1×(−2)

​  

)

P(x,y)=(8,4)

Hence, the required point is (8,4).

Answer 2

let,

A=(-3,5) and B=(2,-5)

point P divides the line segment in 2:3 ratio

W.K.T(we know that)

$p(x,y) = (\frac{m_{1}x_{2} + m_{2}x_{1}}{ m_{1} m_{2}} , \frac{m_{1}y_{2} + m_{2}y_{1}}{m_{1} m_{2}} ) \\ p(x,y) =( \frac{2 \times 2 + 3 \times - 3}{2 \times 3} , \frac{2 \times (- 5) + 3 \times 5}{2 \times 3} ) \\ = ( \frac{4 - 9}{6} , \frac{ - 10 + 15}{6} ) \\ = ( \frac{ - 5}{6} , \frac{ 5}{6} )$

therefore coordinates of point P =(-5/6,5/6)