Question

Find the coordinates of the point which divides the line segment joining the points (0, 3) and (-1, 2) in the ratio 1 : 2.​

Answer 1

Step-by-step explanation:

Given coordinates are (0,3) and (-1,2) . We have to find the coordinates of the points which divides the line segment joining the given coordinates in the ratio 1 : 2.

Let's assume that,

• (0, 3) = ( x1, y1 )
• (-1, 2) = (x2, y2)
• 1 : 2 = m1 : m2

Now, we have a formula to find the coordinates of the points which divides the line segment joining the given coordinates in the ratio of m1 : m2 :

• $\rm(x,y) = \left(\dfrac{m_1x_2+m_2x_1}{m_1+m_2},\dfrac{m_1y_2+m_2y_1}{m_1+m_2}\right)$

By substituting the known values of variable, we get:

$\rm \implies(x,y) = \left(\dfrac{m_1x_2+m_2x_1}{m_1+m_2},\dfrac{m_1y_2+m_2y_1}{m_1+m_2}\right)$

$\rm \implies (x,y) = \left(\dfrac{(1)( - 1)+(2)(1)}{1 + 2},\dfrac{(1)(2)+(2)(3)}{1 + 2}\right)$

$\rm \implies (x,y) = \left(\dfrac{ - 1 + 2}{3},\dfrac{2 + 6}{3}\right)$

$\rm \implies (x,y) = \left(\dfrac{1}{3},\dfrac{8}{3}\right)$

These are the required coordinates.