Question

The co-ordinates of the point which divides the line joining $(1,-2)$ and $(4,7)$ internally in the ratio $1:2$ are

• A. $(1,2)$
• B. $(-1,-1)$
• C. $(-1,2)$
• D. $(2,1)$

Answer 1

Answer: (D)

$(2,1)$

We know if a point divides the line segment $AB$ joining two points $A(x_1,y_1)$ and $B(x_2,y_2)$ in given ratio m:n internally, then by section formula, the cordinates of a point are given as

$=(\frac{m{x}_2+n{x}_1}{m+n},\frac{m{y}_2+n{y}_1}{m+n})$

Since the points $(1,-2)$ and $(4,7)$ divides internally in the ratio

$1:2$, then the coordinates of the point can be determined as follows:

$(x,y)=(\frac{1\times 4+2\times 1}{1+2},\frac{1\times 7+2\times -2}{1+2})=(\frac{4+2}{3},\frac{7-4}{3})=(\frac{6}{3},\frac{3}{3})=(2,1)$