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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
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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