Question

the coordinates of a point dividing the join of the points (5, 0) and (0, 4) in the ratio 2:3 internally are​

Answer 1

Answer:

Let A(5,0) and B(0,4) be the coordinates of the line.

Ratio = 2:3

Therefore coordinates of the point dividing the line AB = (3,8/5)

See the attached image for better understanding

Answer 2

Complete question:

Find the coordinates of the point which divides the line segment joining the points (5, 0) and (0, 4) in the ratio 2 : 3 internally are :

The coordinates of the point which divides the line segment joining the points (5, 0) and (0, 4) in the ratio 2 : 3 internally are $(3 , \frac{8}{5})$

Given: The line segment joins the points (5, 0) and (0, 4) in the ratio 2 : 3 internally.

To find : The coordinates of the point which divides the line segment

Formula used:

Section Formula :

$P (x,y) = ( \frac{m_1 x_2 \ + \ m_2 x_1}{m_1 \ + \ m_2} , \frac{m_1y_2\ + \ m_2y_1}{m_1 \ + \ m_2})$

Solution:

Step 1: Write the given values in  $m_1, m_2 , x_1 , y_1, x_2, y_2$

Let P(x, y) be the required point.

P divides AB internally in the ratio 2 : 3

Here, $m_1= 2, m_2 = 3 , x_1 = 5, y_1= 0, x_2 = 0 , y_2 = 4$

Step 2 : Find the value of P by section Formula:

$P (x,y) = ( \frac{m_1 x_2 \ + \ m_2 x_1}{m_1 \ + \ m_2} , \frac{m_1y_2\ + \ m_2y_1}{m_1 \ + \ m_2})$

$P (x,y) = ( \frac{2\ \times \ 0 \ + \ 3 \ \times \ 5}{2\ +\ 3} , \frac{2\ \times \ 4 \ + \ 3 \ \times \ 0}{2\ +\ 3})$

$P= \frac{0\ + \ 15}{5} ,\frac{8\ + \ 0}{5}\\\\\ P= (\frac{15}{5} , \frac{8}{5} )\\\\\ P= (3 , \frac{8}{5} )$

Hence the coordinates of the point which divides the line segment joining the points (5, 0) and (0, 4) in the ratio 2 : 3 internally are $(3 , \frac{8}{5})$ .

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