Answer:
XY = 5[tex]\sqrt{2}[/tex]
Step-by-step explanation:
Calculate the coordinates of X and Y using the midpoint formula
[ [tex]\frac{1}{2}[/tex](x₁ + x₂), [tex]\frac{1}{2}[/tex](y₁ + y₂) ]
with (x₁, y₁ ) = A(- 3, 9) and (x₂, y₂ ) = B(- 5, - 3)
X = [[tex]\frac{1}{2}[/tex](- 3 - 5), [tex]\frac{1}{2}[/tex](9 - 3) ] = (- 4, 3)
Repeat with
(x₁, y₁ ) = B(- 5, - 3) and (x₂, y₂ ) = C(7, - 1)
Y = [ [tex]\frac{1}{2}[/tex](- 5 + 7), [tex]\frac{1}{2}[/tex](- 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 = [tex]\sqrt{(1 +4)^2+(-2-3)^2}[/tex]
= [tex]\sqrt{5^2+(-5)^2}[/tex]
= [tex]\sqrt{25+25}[/tex] = [tex]\sqrt{50}[/tex] = 5[tex]\sqrt{2}[/tex]
