Question

Find the distance between the pair of points: (3,1) and (4,-5).

Answer 1

9.2195445 (9.22 rounded)

Explanation:

#1: Use the distance formula to determine the distance between the two points:

Distance =
`\sqrt{(x_(2)-x_(1))^(2)+(y_(2)-y_(1))^(2)}`

#2: Substitute the actual values of the points into the distance formula:

`\sqrt{((-4)-3)^(2)+(5-(-1))^(2)}`

#3: Simplify:

- Subtract 3 from -4:
`\sqrt{(-7)^(2)+(5-(-1))^(2)}`

- Raise -7 to the power of 2:
`\sqrt{49+(5-(-1))^(2)}`

- Multiply -1 by -1:
`\sqrt{49+(5+1)^(2)}`

- Add 5 and 1:
`\sqrt{49+6^(2)}`

- Raise 6 to the power of 2:
`√(49+36)`

- Add 49 and 36:
`√(85)` (Decimal form: 9.2195445 (9.22 rounded))

The distance between the two points (3,1) and (4,-5) is 9.22.