Answer:
9.2195445 (9.22 rounded)
Step-by-step explanation:
#1: Use the distance formula to determine the distance between the two points:
Distance = [tex]\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]
#2: Substitute the actual values of the points into the distance formula:
[tex]\sqrt{((-4)-3)^{2}+(5-(-1))^{2}}[/tex]
#3: Simplify:
- Subtract 3 from -4: [tex]\sqrt{(-7)^{2}+(5-(-1))^{2}}[/tex]
- Raise -7 to the power of 2: [tex]\sqrt{49+(5-(-1))^{2}}[/tex]
- Multiply -1 by -1: [tex]\sqrt{49+(5+1)^{2}}[/tex]
- Add 5 and 1: [tex]\sqrt{49+6^{2}}[/tex]
- Raise 6 to the power of 2: [tex]\sqrt{49+36}[/tex]
- Add 49 and 36: [tex]\sqrt{85}[/tex] (Decimal form: 9.2195445 (9.22 rounded))
The distance between the two points (3,1) and (4,-5) is 9.22.
