Question

HELP
Suppose A has a coordinate of 8 and AB = 3. What are the possible midpoints of AB?

Answer 1

Answer:

The possible midpoints of AB are $\frac{19}{2}$ and $\frac{13}{2}$.

Step-by-step explanation:

Let suppose that A and B have one-dimensional coordinates. GIven that $A = 8$ and $AB = 3$, there are two possible locations for B:

$B_{1} = A+AB$

$B_{1} =8+3$

$B_{1} = 11$

$B_{2} = A-AB$

$B_{2} = 8-3$

$B_{2} = 5$

The midpoint equations for each case are, respectively:

$m_{1} = \frac{A+B_{1}}{2}$

$m_{1}=\frac{8+11}{2}$

$m_{1} = \frac{19}{2}$

$m_{2} = \frac{A+B_{2}}{2}$

$m_{2} = \frac{5+8}{2}$

$m_{2} = \frac{13}{2}$

The possible midpoints of AB are $\frac{19}{2}$ and $\frac{13}{2}$.