Question

Find the co - ordinate of the point which divide the line segment joining the points (2,3) and (7,8) internally in the Ration 2:3

Answer 1

Answer

The coordinates of the required point is (4 , 5)

$\bf\large\underline{Given}$

• The points are (2 , 3) and (7 , 8)
• The other point divides the given points internally in the ratio of 2:3

$\bf\large\underline{To \ Find}$

• The coordinates of the points which point divides the points (2 , 3) and (7 , 8)

$\bf\large\underline{Formula \ to \ be \ used}$

If ( x₁ , y₁) and (x₂ , y₂) are two points and another point (x , y) divides these points in ratio m:n then

$\tt x = \dfrac{m x_{2} - nx_{1}}{m + n} \: \: , \: \: y = \dfrac{my _{2} - ny_{1} }{m + n}$

$\bf\large\underline{Solution}$

Let us consider the givens points as A(2 , 3) and B(7 , 8)

and the point divides line AB in ratio 2:3 be (x , y)

Therefore , by section formula

For X-coordinates

$\sf \implies x = \dfrac{2\times 7 + 3\times2}{2+3} \\\\ \sf\implies x = \dfrac{14+6}{5} \\\\ \sf\implies x = \dfrac{20}{5} \\\\ \sf\implies x = 4$

For Y-coordinates

$\sf\implies y = \dfrac{2\times8 + 3\times3}{2+3} \\\\ \sf\implies y = \dfrac{16+9}{5} \\\\ \sf\implies y = \dfrac{25}{5} \\\\ \sf\implies y = 5$

Hence , the required coordinates of the point is (4 , 5)

Answer 2

Answer

The coordinates of the given point is (4,5)

Given

• The points are ( 2,3) and ( 7,8 )

• The other point divides the given points internally in the ratio of 2:3

To Find

• The coordinates of the points which point divides the points ( 2,3 ) and ( 7,8 )

Formula to be used

If (x1 , y1) and (x2, y2) are two points and another point (x, y) divides these points into ratio m:n then

x = mx2 - nx1/m+n , y = my2 - ny1/ m+n

Solution

Let us consider the givens points as A(2,3) and B(7,8)

And the point divides line AB in ratio 2:3 be (x, y)

Therefore, by section formula

For X-coordinates

➡️ x = 2•7+3•2/ 2+3

➡️ x = 14 +6/5

➡️ x = 20/5

➡️ x = 4

For Y-coordinates

➡️ y = 2•8+3•3/2+3

➡️ y = 16+9/5

➡️ y = 25/5

➡️ y = 5

Hence the required coordinates of the point is (4,5).