Answered

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What is the distance of
CD

given that
C (5,-2) and D (-3,8)
Leave your answer as a square root.

Sagot :

Answer:

CD = [tex]\sqrt{164}[/tex]

Step-by-step explanation:

Calculate the distance d using the distance formula

d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = C(5, - 2) and (x₂, y₂ ) = (D(- 3, 8)

d = [tex]\sqrt{(-3-5)^2+(8+2)^2}[/tex]

   = [tex]\sqrt{(-8)^2+10^2}[/tex]

    = [tex]\sqrt{64+100}[/tex]

    = [tex]\sqrt{164}[/tex]

     = 2[tex]\sqrt{41}[/tex] ← in simplest form

BrainlyRonaldo

Given :

  • C (5, - 2)
  • D (- 3, 8)

To Find :

  • CD = ?

Solution :

As, we have C (5, - 2) and D (- 3, 8), to find CD let's use distance formula :

[tex] \underline{\boxed{\tt{Distance \: between \: two \: points = \sqrt{(x_2 - x_1)^{2} + (y_2 - y_1)^{2}}}}}[/tex]

Here,

  • x₁ = 5
  • x₂ = - 3
  • y₁ = - 2
  • y₂ = 8

So, by filling values :

[tex] \sf : \implies CD = \sqrt{(-3 - 5)^{2} + (8 - (-2))^{2}}[/tex]

[tex] \sf : \implies CD = \sqrt{(-8)^{2} + (8 +2))^{2}}[/tex]

[tex] \sf : \implies CD = \sqrt{64 + (10)^{2}}[/tex]

[tex] \sf : \implies CD = \sqrt{64 + 100}[/tex]

[tex] \sf : \implies CD = \sqrt{164}[/tex]

Hence, distance of CD is [tex] \bold{\sf \sqrt{164}.}[/tex]

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