Question

How do you determine the length ?

Answer 1

XY = 5
`√(2)`

Explanation:

Calculate the coordinates of X and Y using the midpoint formula

[
`(1)/(2)`(x₁ + x₂),
`(1)/(2)`(y₁ + y₂) ]

with (x₁, y₁ ) = A(- 3, 9) and (x₂, y₂ ) = B(- 5, - 3)

X = [
`(1)/(2)`(- 3 - 5),
`(1)/(2)`(9 - 3) ] = (- 4, 3)

Repeat with

(x₁, y₁ ) = B(- 5, - 3) and (x₂, y₂ ) = C(7, - 1)

Y = [
`(1)/(2)`(- 5 + 7),
`(1)/(2)`(- 3 - 1) ] = (1, - 2)

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Calculate the length of XY using the distance formula

d = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = X(- 4, 3) and (x₂, y₂ ) = Y(1, - 2)

XY =
`√((1 +4)^2+(-2-3)^2)`

=
`√(5^2+(-5)^2)`

=
`√(25+25)` =
`√(50)` = 5
`√(2)`