- Distance Formula: [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
- Product Rule of Radicals: √ab = √a × √b
- Midpoint Formula: [tex](\frac{x_2+x_1}{2},\frac{y_2+y_1}{2})[/tex]
Firstly, to get the distance, plug the points into the distance formula to solve as such:
[tex]\sqrt{(6-2)^2+(9-5)^2}\\\sqrt{4^2+4^2}\\\sqrt{16+16}\\\sqrt{32}[/tex]
Now our answer may be √32, however we can simplify it as such (thanks to the product rule of radicals):
√32 = √16 × √2 = 4√2.
The distance is 4√2, or approximately 5.66 units.
Next, to get the midpoint plug in the points into the midpoint formula and solve as such:
[tex](\frac{2+6}{2},\frac{5+9}{2})\\\\(\frac{8}{2},\frac{14}{2})\\\\(4,7)[/tex]
The midpoint is (4,7).
