Question

Point Rdivides Poin the ratio 1:3. If the x coordinate of Ris 1 and the x coordinate of Pis-3, what is the x coordinate ofA.13B. 3C. 5D. 6E 9

Answer 1

You know that:

- Point R divides PQ in this ratio:

$1\colon3$

- The x-coordinate of Point R is:

$x_R=-1$

- The x-coordinate of Point P is:

$x_P=-3$

Then, you can make this drawing (it is not drawn to scale).

The Internal Section Formula for the x-coordinate of the point that divides the segment is:

$x=\frac{m_{}x_2-nx_1}{m-n}$

Where the coordinates of the endpoints are:

$\begin{gathered} (x_1,y_1) \\ (x_2,y_2) \end{gathered}$

And the segment is divided internally in the ratio:

$m\colon n_{}$

In this case, you can identify that:

$\begin{gathered} x_2=x_P=-3 \\ \\ x=-1 \\ \\ m=1 \\ \\ n=3 \end{gathered}$

Then, you can substitute values and solve for:

$x_1$

Which, in this case, is the x-coordinate of Point Q.

Then, you get:

$\begin{gathered} -1=\frac{(1)_{}(-3)_{}-(3)x_1}{1-3} \\ \\ -1=\frac{-3_{}-3x_1}{-2} \end{gathered}$$undefined$