Question

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

Answer 1

The distance is 9.2195 (9.22 rounded)

Answer 2

Answer:

9.2195445 (9.22 rounded)

Step-by-step 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: $\sqrt{49+36}$

- Add 49 and 36: $\sqrt{85}$ (Decimal form: 9.2195445 (9.22 rounded))

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