Answer
a) M(6,2)
b) 𝘈𝘉= 10
Work Step by Step
1) You are given the points A(3,6) and B(9,-2)
2) We determine the midpoint using the midpoint formula
m=$(\frac{x_{1}+x_{2}}{2}$, $\frac{y_{1}+y_{2}}{2})$= $(\frac{3+9}{2}$, $\frac{6-2}{2})$
3) This simplifies into:
$(\frac{12}{2}$, $\frac{4}{2})$= (6, 2)
4) Next, you use distance formula to get the total length of AB
d=$\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}$
5) Plug in the coordinates
d=$\sqrt{(9-3)^{2}+(-2-6)^{2}}$=$\sqrt {100}$=10
6) Therefore, the midpoint of line 𝘈𝘉 is at (6,2) and the line's length is 10 units
