Question

A is the point (-2,4) and B is the point (7,1). Find the length of AB giving your answer in its simplest surd form.​

Answer 1

AB = 3
`√(10)`

Explanation:

Calculate AB using the distance formula

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

with (x₁, y₁ ) = A (- 2, 4) and (x₂, y₂ ) = B (7, 1 )

AB =
`√((7-(-2))^2+(1-4)^2)`

=
`√((7+2)^2+(-3)^2)`

=
`√(9^2+9)`

=
`√(81+9)`

=
`√(90)`

=
`√(9(10))`

=
`√(9)` ×
`√(10)`

= 3
`√(10)`