Question

What is the distance from (-5,2) and (0,4)?

Answer 1

Answer:
`\Large\boxed{Distance=√(29) }`

Explanation:

Given information

`(x_1,~y_1)=(-5,~2)`

`(x_2,~y_2)=(0,~4)`

Given the distance formula

`Distance =√((x_2-x_1)^2+(y_2-y_1)^2)`

Substitute values into the formula

`Distance =√(((0)-(-5))^2+((4)-(2))^2)`

Simplify values in the parenthesis

`Distance =√((0+5)^2+(4-2)^2)`

`Distance =√((5)^2+(2)^2)`

Simplify the exponents

`Distance =√(25+4)`

Simplify values in the radical sign

`\Large\boxed{Distance =√(29)\approx5.4}`

Hope this helps!! :)

Please let me know if you have any questions

Answer 2

d =
`√(29)`

Explanation:

The distance between two points is given by

d =
`√( ( x2 - x1) ^2 - ( y2-y1)^2)` where ( x1,y1) and ( x2,y2) are the two points

d =
`√(( 0 - -5) ^2 + (4 - 2) ^2)`

d =
`√(5^2 + 2^2)`

d =
`√(25 +4)`

d =
`√(29)`