Question

Find the cor-ordinates of the points which
devides the line segment Joining the points
(-1,3) and (5,4)internaly ratio 1:2​

Answer 1

Question :-

Find the cor-ordinates of the points which

devides the line segment Joining the points

(-1,3) and (5,4) internally ratio 1:2.

Answer :-

• The co-ordinate is $1, \frac{10}{3}$

Step by step explanation :-

Using the section formula, if a point $\rm{(x,y) }$ divides the line joining the points $\rm{(x_1 , y_1) }$ and $\rm{(x_2 , y_2) }$ in the ratio $\rm{m :n }$ , then

$\rm:\longmapsto{(x, y) = \bigg( \frac{mx_2 + nx_1 }{m+n} , \frac{my_2 + ny_1 }{m+n} \bigg)}$

Let, $\rm{(a,b)}$be the point which divides the line segment joining points $(-1,3)$ and

$(5,4)$ in the ratio 1:2 internally.

By section formula,

$\rm:\longmapsto{(a, b) = \bigg( \frac{(1 \times 5) + (2 \times - 1)}{1 + 2} , \frac{(1 \times 4) + (2 \times 3)}{1 + 2} \bigg) } \\ \\ \rm:\longmapsto{(a, b) = \bigg( \frac{5 + ( - 2)}{3} , \frac{4 + 6}{3} \bigg) } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \rm:\longmapsto{(a, b) = \bigg( \frac{ 3 }{3} , \frac{10}{3} \bigg) } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bf:\longmapsto \red{(a, b) = \bigg( 1, \frac{10}{3} \bigg) } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

Hence, $1 , \frac{10}{3}$ is the origin divides the line segment $\rm{( - 1, 3)}$ and $(5, 4)$ in the ratio $1 : 2$ internally.

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