Question

given p (3, 7) and q(11, 15), find the coordinates of the point r that divides pq in the ratio 1 : 3.

Explanation:

Step1: Recall section - formula

The formula for the coordinates of a point \(R(x,y)\) that divides the line - segment joining \(P(x_1,y_1)\) and \(Q(x_2,y_2)\) in the ratio \(m:n\) is \(x=\frac{mx_2+nx_1}{m + n}\) and \(y=\frac{my_2+ny_1}{m + n}\). Here, \(x_1 = 3,y_1 = 7,x_2 = 11,y_2 = 15,m = 1,n = 3\).

Step2: Calculate the \(x\) - coordinate of \(R\)

$$
LATEXBLOCK0
$$

Step3: Calculate the \(y\) - coordinate of \(R\)

$$
LATEXBLOCK1
$$

Answer:

A. \((5,9)\)