Question

5) Find the co-oridinates of the point which
divides the
Join (2, 1) and (7,6) in the
natio 3:2​

Answer 1

✬ The co ordinates of the point is (5,4) ✬

Step-by-step explanation:

Given: The co-oridinates of the point which divides the line segment joining the points (2, 1) and (7,6) in the ratio 3:2.

To find: The co ordinates of the point

Required Formula:

$\\ \: \: \: \ \: \bullet \: \: \sf{ \overline{AB} = \bigg(\frac{mx_2 + nx_1 }{m + n},\frac{my_2+ny_1}{m+n} \bigg)}$

Solution:

Let A(x₁,y₁) = (2,1) and B(x₂,y₂) = (7,6).

• Given ratio m:n = 3:2

Applying the values,

$\\ \longmapsto\sf{AB = \bigg(\frac{3\times7+2\times2}{3+2} ,\frac{3 \times 6 + 2 \times 1}{3 + 2} \bigg)} \\ \\ \longmapsto\sf{AB = \bigg( \frac{21 + 4}{5}, \frac{18 + 2}{5} \bigg)} \\ \\ \longmapsto\sf{AB = \bigg( \frac{25}{5}, \frac{20}{5} \bigg)} \\ \\ \longmapsto\sf{AB = \bigg(5,4 \bigg)}$

• Hence,The co-ordinate of the point is (5,4).