Question

The ratio in which the y-axis divides the line joining M(-2, 2) and N(4, 5) is:

• A. 1 : 2
• B. 2 : 3
• C. 1 : 3
• D. 1 : 4

Answer 1

The correct option is A 1 : 2

Let the point on the y-axis that divides the line joining M(-2, 2) and N(4, 5) be P(0, y).
Let P(0, y) divide MN in the ratio k : 1.

Thus, by section formula,
$P(0,y)=\frac{[kx2+x1]}{[k+1]},\frac{[ky2+y1]}{[k+1]}$
where $(x_1,y_1)=(-2,2)and(x_2,y_2)=(4,5)$
Hence, $\frac{(4k-2)}{(k+1)}=0$
$\Rightarrow k=\frac{1}{2}$
Thus, the y-axis divides MN in the ratio 1 : 2.