Question

The point $(8,4)$ divides the line joining $(5,-2)$ and $(9,6)$ in the ratio

• A. $-3:1$
• B. $3:-1$
• C. $3:1$
• D. $1:3$

Answer 1

The correct option is C $3:1$

Given point (8, 4) = C x , y

Let $A(5,-2)B(9,6)$

$x_1{y}_1{x}_2{y}_2$

we have to find the

ratio of AC & CB

Let ratio = k : 1

$m_1:m_2=k:1$

using section formula

$x=\frac{m_1{x}_2+m_2{x}_1}{m_1+m_2}$

$8=\frac{k\left(9\right)+1\left(5\right)}{1+k}$

$8=(1+k)=9k+5$

$9k+5-8-8k=0$

$k=3$

The ratio is $k:1$

$=3:1$