Question

If a=p-2, m=22, and b=p+8 then p=? a=? b=?

Answer 1

Given:

a = p- 2

m = 22

b = p + 8

Using midpoint formula:

`\begin{gathered} m\text{ = }(a+b)/(2) \\ \\ 22\text{ = }((p-2)+(p+8))/(2) \\ \text{multiply both sides by 2:} \\ \\ 22\ast2=\text{ }(p-2)+(p+8) \\ \\ 44\text{ = p-2+p+8} \\ \\ 44\text{ = p + p - 2 + 8} \\ \\ 44\text{ = 2p + 6} \\ \\ 2p\text{ = 44 - 6} \\ \\ 2p\text{ = 38} \\ \\ p\text{ = }(38)/(2) \\ \\ p\text{ = 19} \\ \\ Since\text{ P = 19, substitute p for 19 in a = p-2 and b = p+8} \\ \\ \text{THus,} \\ a\text{ = p - 2 = 19 - 2= 17} \\ a\text{ = 17} \\ \\ b\text{ = p + 8 = 19 + 8 = 27} \\ b\text{ = 27} \end{gathered}`

`\begin{gathered} \text{ANSWER:} \\ p\text{ = 19} \\ a\text{ = 17} \\ b\text{ = 27} \end{gathered}`