Question

42
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

For a point dividing a segment $PQ$ in ratio $m:n$, the x-coordinate is $x_R = \frac{m x_Q + n x_P}{m + n}$, where $m=1$, $n=3$, $x_R=-1$, $x_P=-3$.

Step2: Substitute known values

$$-1 = \frac{1 \cdot x_Q + 3 \cdot (-3)}{1+3}$$

Step3: Simplify denominator and multiply

$$-1 = \frac{x_Q - 9}{4}$$
Multiply both sides by 4: $-4 = x_Q - 9$

Step4: Solve for $x_Q$

$$x_Q = -4 + 9 = 5$$

Answer:

C. 5