Question

The coordinates of two points A and B are $(-1,7)$ and $(4,-3)$. Then the coordinates of the point P on AB such that AP:PB = 2:3 are

• A. $(-1,-3)$
• B. $(1,3)$
• C. $(1,-3)$
• D. $(-1,3)$

Answer 1

The correct option is B

$(1,3)$

We calculate the coordinates of a point dividing the line joining two points $A(-1,7)$ and $B(4,-3)$ in the ratio 2:3.

Let the coordinates of this point be $(x,y)$

Then the part of the line from $(-1,7)$ to $(x,y)$ is $\frac{2}{5}$ (which we call as $\frac{p}{w}$) of the whole line.

Then,

$x=x_1+\frac{p}{w}(x_2-x_1)=-1+\frac{2}{5}(4-(-1\left)\right)=1$

$y=y_1+\frac{p}{w}\left(y_2-y_1\right)=7+\frac{2}{5}(-3-7)=3$

$\therefore$ The point is $(1,3)$