Answer:
[tex]\sqrt{34}[/tex] (or 5.83 when rounded to the nearest hundredth)
Step-by-step explanation:
Key skills needed: Distance Formula/ Pythagorean Theorem
1) There are 2 ways to approach this problem
- Pythagorean Theorem
- Distance formula
2) Let's use distance formula first (I will explain both ways
- Distance formula is --> Given 2 points: [tex](x_1, y_1)[/tex] & [tex](x_2, y_2)[/tex] the distance between these 2 points is [tex]\sqrt{(x_1-x_2)^2 + (y_1-y_2)^2}[/tex]
- The 2 points here are: S (3,2) and W (-2,-1)
- 3 would be [tex]x_1[/tex], 2 would be [tex]y_1[/tex], -2 would be [tex]x_2[/tex], -1 would be [tex]y_2[/tex]
- This means the distance would be:
[tex]\sqrt{(3-(-2))^2 + (1-(-2))^2}[/tex] 3- (-2) is 3 + 2 = 5 .... 1 - (-2) = 1 + 2 = 3
So it would be [tex]\sqrt{5^2 + 3^2}[/tex] (5 squared is 25 and 3 squared is 9)
--> [tex]\sqrt{25 + 9}[/tex] = [tex]\sqrt{34}[/tex] ---> Around 5.83 when rounded to the nearest hundredth
3) The next way is via pythagorean theorem
- The pythagorean theorem is --> [tex]a^2 + b^2 = c^2[/tex]
- "a" would be 5 (since from W to S you move 5 units to the right) and "b" would be 3 (since from W to S you move 3 units up). "c" is the distance we need to find
- [tex]5^2 + 3^2 = c^2[/tex] (5 squared plus 3 squared is 25 + 9 = 34)
--> [tex]34 = c^2[/tex] --> take the square root of both sides and get --> [tex]c = \sqrt{34}[/tex]
The square root of 34 is around 5.83 units when rounded to the nearest hundredth.
Sorry to keep you waiting but hope you understood and have a nice day!! :D
