Question

The coordinates of the point P which divides the line joining the points (-1,-4) (8,6) internally in the ratio 3:2 is
(a) 22/5, 2
(b) 13/3,4
(c) 12/5,3
(d) 25/3,7​

Answer 1

Answer:

$\rm \: (a) \: \dfrac{22}{5} \: ,2$

Explanation:

Given points,

• $\rm (x_1 \:\&\: y_1)$ =(-1, -4)
• $\rm (x_2 \:\&\: y_2)$ = (8, 6)

Where, point P divides them in the ratio$\rm (m_1 \:\&\: m_2)$ 3 : 2.

By section formula,

${ = \rm \bigg \{ \dfrac{m_1x_2 + m_2x_1}{ m_1 + m_2} ,\: \dfrac{m_1y_2 + m_2y_1}{m_1 + m_2} \bigg\}}$

On substituting the values,

${ = \rm \bigg \{ \dfrac{3(8) + 2( - 1)}{ 3 + 2} ,\: \dfrac{3(6) + 2( - 4)}{3 + 2} \bigg\}}$

${ = \rm \bigg \{ \dfrac{24 - 2}{ 5} ,\: \dfrac{18 - 8}{5} \bigg\}}$

${ = \rm \bigg \{ \dfrac{22}{ 5} ,\: \dfrac{10}{5} \bigg\}}$

${ = \rm \bigg \{ \dfrac{22}{ 5} ,\: 2 \bigg\}}$

Required answer : $\rm \dfrac{22}{5},\: 2$