Question

The coordinates of two points A and B are $(-3,5)$ and $(4,-9)$. Then the coordinates of the point P on AB such that AP:PB = 1:6 are

• A. (2, -3)
• B. (-2, 3)
• C. (2, 3)
• D. (-2, -3)

Answer 1

The correct option is B

(-2, 3)

We calculate the coordinates of a point dividing the line joining two points $A(-3,5)$ and $B(4,-9)$ in the ratio 1:6.

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

Then the part of the line from $(-3,5)$ to $(x,y)$ is $\frac{1}{7}$(which we call as $\frac{p}{w}$) of the whole line.

Then,

$x=x_1+\frac{p}{w}(x_2-x_1)=-3+\frac{1}{7}(4-(-3\left)\right)=-2$

$y=y_1+\frac{p}{w}(y_2-y_1)=5+\frac{1}{7}(-9-5)=3$

$\therefore$ The point is $(-2,3)$