Question

The ratio in which x axis divides the line segment joining the points (6 , 4) and (1 ,- 7) is m : n. Find the value of mn.

• A. 50
• B. 45
• C. 36
• D. 28

Answer 1

The correct option is D 28

Let p(x,0) be the point on the x axis.

Let k : 1 be the ratio of the line segment joining the points (6,4) and (1,-7) and

The coordinates of P (x, 0) are
$p(x,0)=(\frac{1\times k+1\times 6}{k+1},\frac{k\times -7+1\times 4}{k+1})=(\frac{k+6}{k+1},\frac{-7k+4}{k+1})$

$\Rightarrow -7k+4=0$

$\Rightarrow k=\frac{4}{7}$.

Hence, k : 1 = m : n = $\frac{4}{7}$ : 1
= 4 : 7

Therefore, mn = 4 x 7 = 28