Answer:
[tex]Q =2\frac{1}{2}[/tex] or [tex]Q =- 10\frac{1}{2}[/tex]
Step-by-step explanation:
Given
[tex]P = -4[/tex] --- missing from the question
[tex]Distance = 6\frac{1}{2}[/tex]
Required
Determine the possible value of Q
The distance can be calculated using absolute function as:
[tex]Distance = |Q - P|[/tex]
Substitute values for distance and P
[tex]6\frac{1}{2} = |Q - (-4)|[/tex]
[tex]6\frac{1}{2} = |Q +4|[/tex]
The absolute function can then be split as:
[tex]6\frac{1}{2} = Q + 4[/tex] or [tex]-6\frac{1}{2} = Q + 4[/tex]
Make Q the subject in both cases:
[tex]Q = 6\frac{1}{2} - 4[/tex] or [tex]Q = -4 - 6\frac{1}{2}[/tex]
[tex]Q =2\frac{1}{2}[/tex] or [tex]Q =- 10\frac{1}{2}[/tex]
