Question

What is the exact distance from (-5,1) to (3,0).

Answer 1

The distance between the two points is
`√(65) \ \text{units}.`

Explanation:

In order to find the distance between two coordinate pairs, we can use the distance formula:

`\displaystyle \bullet \ \ \ d = √((x_2-x_1)^2+(y_2-y_1)^2)`

Our coordinate pairs need to be labeled accordingly, so we can use this naming system:

`\bullet \ \ \ (x_1, y_1), (x_2, y_2)`

This assigns a name to our points:

• 
  `x_1 = -5`
• 
  `y_1 = 1`
• 
  `x_2 = 3`
• 
  `y_2 = 0`

Therefore, we can plug these into the formula and solve:

`d=√((3-(-5))^2+(0-1)^2)\\\\d=√((8)^2+(-1)^2)\\\\d=√(8^2+1^2)\\\\d=√(64+1)\\\\d=√(65)`

Therefore, the distance between the two points is
`√(65) \ \text{units}`.