Question

Calculate the ratio in which the line joining the points A(-1, 2) and B(5, 7) is divided by the line represented by the equation x = 2.

• A. 4 : 5
• B. 3 :2
• C. 1 : 1
• D. 9 : 4

Answer 1

The correct option is C 1 : 1

Every point on the line represented by the equation x = 2 can be expressed as (2, y) where y is the y-coordinate.

Let (2, y) be the point on the line represented by the equation x = 2 which divides the line joining the points A(-1, 2) and B(5, 7).

Let the required ratio be k : 1.

The coordinates of the point that divides a line joining the points $(x_1,y_1)$ and $(x_2,y_2)$ in the ratio m : n are

$(\frac{n\times x_1+m\times x_2}{m+n},\frac{n\times y_1+m\times y_2}{m+n})$

$\Rightarrow 2=\frac{5k+1(-1)}{k+1}$

$\Rightarrow 2k+2=5k-1$

$\Rightarrow 3k=3$

$\Rightarrow k=1$

Therefore, the required ratio is 1:1.