# Find the coordinates of the point which divides

Question:

Find the coordinates of the point which divides the line segment joining (−1,3) and (4, −7) internally in the ratio 3 : 4

Solution:

We have A (−1, 3) and B (4,−7) be two points. Let a pointdivide the line segment joining the points A and B in the ratio 3:4 internally.

Now according to the section formula if point a point P divides a line segment joining andin the ratio m: n internally than,

$\mathrm{P}(x, y)=\left(\frac{m x_{1}+m x_{2}}{m+n}, \frac{m y_{1}+m y_{2}}{m+n}\right)$

Now we will use section formula to find the co-ordinates of unknown point P as,

$\mathrm{P}(x, y)=\left(\frac{4(-1)+3(4)}{3+4}, \frac{4(3)+3(-7)}{3+4}\right)$

$=\left(\frac{8}{7},-\frac{9}{7}\right)$

Therefore, co-ordinates of point $\mathrm{P}$ is $\left(\frac{8}{7},-\frac{9}{7}\right)$

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