Question

Find the distance and the midpoint of the line segment with endpoints (-1,4) and (-5,3)

i already know the answer i just need an explanation

Answer 1

see explanation

Explanation:

Calculate the distance (d) using the distance formula

d = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (- 1,4) and (x₂, y₂ ) = (- 5, 3)

d =
`√((-5+1)^2+(3-4)^2)`

=
`√((-4)^2+(-1)^2)`

=
`√(16+1)` =
`√(17)` ≈4.12 ( to 2 dec. places )

To find the midpoint use the midpoint formula

[0.5(x₁ + x₂ ), 0.5(y₁ + y₂ ) ]

Using the same points as above then

midpoint = [0.5(- 1- 5), 0.5(4 + 3 ) ] = [0.5(- 6), 0.5(7) ] = (- 3, 3.5 )