Question

1. (number system) the distance between point q and point p is 6 1/2 units. which number could represent point q?

point p is shown on the number line below.
number line with p at -3 (wait, no, the number line has marks at -12, -10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10, 12, and p is at -3? wait, the number line: the marks are at -12, -10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10, 12. the position of p: looking at the ticks, between -4 and -2, maybe at -3? wait, the original text:
the distance between point q and point p is 6 1/2 units. which number could represent point q?
a -9 1/2
b 1 1/2
c 8 1/2
d 10 1/2
options: a, b, c, d with radio buttons.

Explanation:

Step1: Find position of P

From the number line, point P is at $-4$.

Step2: Calculate possible Q values

Distance formula: $|Q - (-4)| = 6\frac{1}{2}$. So $Q + 4 = \pm6.5$.
Case1: $Q + 4 = 6.5 \Rightarrow Q = 2.5$ (not an option).
Case2: $Q + 4 = -6.5 \Rightarrow Q = -10.5 = -9\frac{1}{2}$ (matches option A).

Answer:

A. $-9\frac{1}{2}$