Question

point r divides $overline{pq}$ 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: Recall section - formula

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

Step2: Substitute values into formula

Substitute the given values into the formula: \(-1=\frac{1\times x_2+3\times(-3)}{1 + 3}\).

Step3: Simplify the equation

First, simplify the right - hand side of the equation: \(-1=\frac{x_2-9}{4}\).

Step4: Solve for \(x_2\)

Multiply both sides of the equation by 4: \(-1\times4=x_2 - 9\), which gives \(-4=x_2-9\). Then add 9 to both sides: \(x_2=-4 + 9=5\).

Answer:

C. 5