Question

Point A is (3,4) Point B is (-1,-2). Find the coordinates of point Q along the directed line segment AB so that the ratio of AQ to QB is 4 to 2.

Answer 1

Answer:

The Co ordinates of Point Q is (0.33,0).

Step-by-step explanation:

Given,

Co ordinates of Point A = (3,4)

Co ordinates of Point B = (-1,-2)

We have to find out the co ordinates of point Q that divides the line segment in the ratio of 4:2.

Solution,

For finding the co ordinates of Q, we use the section formula.

$Q(x,y)=(\frac{mx_2+nx_1}{m+n}) (\frac{my_2+ny_1}{m+n})$

Here,

$x_1=3\ \ \ x_2=-1\\y_1=4\ \ \ y_2=-2\\m=4\ \ and\ \ n=2$

Now we substitute the given values and get;

$Q(x,y)=(\frac{4\times-1+2\times3}{4+2}) (\frac{4\times-2+2\times4}{4+2})\\\\Q(x,y)=(\frac{-4+6}{6})(\frac{-8+8}{6})\\\\Q(x,y)=(\frac{2}{6})(\frac{0}{6})\\\\Q(x,y)=(0.33,0)$

Hence The Co ordinates of Point Q is (0.33,0).