Question

find the coordinates of the point which divides the line segment joining the points (5, - 2) and( 9,6) internally and externally in the ratio 3 ratio 1

Answer 1

Answer:

Step-by-step explanation:

This is the answer

Hope it helps.

Answer 2

Answer:

Let P(x,y) divides the line joining of the points (5,-2) and (9,6) internally in the ratio 3:1 .

$Here, \:x_{1}=5,\:y_{1}=-2\\x_{2}=9,\:y_{2}=6\\and\:m:n=3:1$

By Section formula:

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

$=\left(\frac{3\times 9+1\times 5}{3+1},\:\frac{3\times 6+1\times (-2)}{3+1}\right)$

$=\left(\frac{27+5}{4},\frac{18-2}{4}\right)$

$=\left(\frac{32}{4},\frac{16}{4}\right)$

$=(8,4)$

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

Let Q(x,y) divides the line joining of the points (5,-2) and (9,6) externally in the ratio 3:1 .

$Here, \:x_{1}=5,\:y_{1}=-2\\x_{2}=9,\:y_{2}=6\\and\:m:n=3:1$

By Section formula:

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

$=\left(\frac{3\times 9-1\times 5}{3-1},\:\frac{3\times 6-1\times (-2)}{3-1}\right)$

$=\left(\frac{27-5}{2},\frac{18+2}{2}\right)$

$=\left(\frac{22}{2},\frac{20}{2}\right)$

$=(11,10)$

$Q(x,y) = (11,10)$

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