Question

point r divides \\( \overline { p q } \\) in the ratio 1:3. if the x - coordinate of r is - 1 and the x - coordinate of p is - 3, what is the x - coordinate of q?
a. \\( - \frac { 1 } { 3 } \\)
b. 3
c. 5
d. 6
e. - 9

Explanation:

Step1: Use the section formula for x - coordinate

The section formula for a point \(R(x)\) that divides the line segment joining \(P(x_1)\) and \(Q(x_2)\) in the ratio \(m:n\) is \(x=\frac{mx_2 + nx_1}{m + n}\). Here, \(m = 1\), \(n=3\), \(x=-1\), \(x_1=-3\).
Substitute the values into the formula: \(-1=\frac{1\times x_2+3\times(-3)}{1 + 3}\).

Step2: Solve the equation for \(x_2\)

First, simplify the right - hand side of the equation: \(-1=\frac{x_2-9}{4}\).
Multiply both sides by 4: \(-1\times4=x_2 - 9\).
So, \(-4=x_2-9\).
Add 9 to both sides: \(x_2=-4 + 9\).

Answer:

B. 3