Question

What is the distance of

CD

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

Answer 1

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 :

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

Here,

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

So, by filling values :

`\sf : \implies CD = \sqrt{(-3 - 5)^(2) + (8 - (-2))^(2)}`

`\sf : \implies CD = \sqrt{(-8)^(2) + (8 +2))^(2)}`

`\sf : \implies CD = \sqrt{64 + (10)^(2)}`

`\sf : \implies CD = √(64 + 100)`

`\sf : \implies CD = √(164)`

Hence, distance of CD is
`\bold{\sf √(164).}`

Answer 2

CD =
`√(164)`

Explanation:

Calculate the distance d using the distance formula

d =
`\sqrt{(x_(2)-x_(1))^2+(y_(2)-y_(1))^2 }`

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

d =
`√((-3-5)^2+(8+2)^2)`

=
`√((-8)^2+10^2)`

=
`√(64+100)`

=
`√(164)`

= 2
`√(41)` ← in simplest form