Question

In what ratio does the point (-4, 6) internally divide the line segment joining the points A(-6, 10) and B(3, -8).

• A. 5:2
• B. 2:5
• C. 7:2
• D. 2:7

Answer 1

The correct option is D

2:7

Let point (-4, 6) divide AB internally in the ratio $m_1:m_2$
Using the section formula
We get, $(-4,6)=(\frac{3m_1-6m_2}{m_1+m_2},\frac{-8m_1+10m_2}{m_1+m_2})$

So, -4=$\frac{3m_1-6m_2}{m_1+m_2}$ and 6=$\frac{-8m_1+10m_2}{m_1+m_2}$

$$\begin{array}{cc}-4m_1-4m_2=3m_1-6m_2& 6m_1+6m_2=8m_1+10m_2\\ -7m_1=-2m_2& 14m_1=4m_2\\ \frac{m_1}{m_2}=\frac{2}{7}& \frac{m_1}{m_2}=\frac{2}{7}\end{array}$$
Therefore, the point (-4, 6) divides the line segment joining the points A (-6, 10) and B (3, -8) in the ratio 2:7