Question

What is the exact distance between points a(-2, 7) and b(6,-5)

Answer 1

4
`√(13)`

Explanation:

Calculate the distance d using the distance formula

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

with (x₁, y₁ ) = (- 2, 7) and (x₂, y₂ ) = (6, - 5)

d =
`√((6-(-2))^2+(-5-7)^2)`

=
`√(6+2)^2+(-12)^2)`

=
`√(8^2+144)`

=
`√(64+144)`

=
`√(208)`

=
`√(16(13))`

= 4
`√(13)`

Answer 2

14.4222

Explanation:

Distance between two points = √(x₂ – x₁)² + (y₂ – y₁)²

Distance between two points = √(6 – -2)² + (-5 – 7)²

√(6 – -2)² + (-5 – 7)²

√8² + (-12)²

√64 + 144

√208

14.4222

I hope this helps