Question

suppose that p and q are points on the number line. if pq = 10 and p lies at 8, where could q be located? if there is more than one location, separate them with commas. location(s) of q :

Explanation:

Step1: Recall distance formula on number line

The distance between two points \( P \) (at \( x_1 \)) and \( Q \) (at \( x_2 \)) on a number line is \( |x_2 - x_1| \). Here, \( x_1 = 8 \), and \( PQ = 10 \), so \( |x_2 - 8| = 10 \).

Step2: Solve the absolute - value equation

Case 1: \( x_2 - 8 = 10 \)
Add 8 to both sides: \( x_2=10 + 8=18 \)
Case 2: \( x_2 - 8=- 10 \)
Add 8 to both sides: \( x_2=-10 + 8=-2 \)

Answer:

-2, 18