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Find the distance between the two points in simplest radical form.
(1, -7) and (7,0)

Sagot :

THManagement

Answer:

The distance between the two given points is equal to √85.

Step-by-step explanation:

Let's recall what the distance formula is:

[tex]\displaystyle \huge\math\boxed{d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2} }[/tex]

We are defined our two points as:

  • (x₁, y₁) → (1, -7)
  • (x₂, y₂) → (7, 0)

We can rewrite this into our different "variables":

  • x₁ = 1
  • y₁ = -7
  • x₂ = 7
  • y₂ = 0

Now given our distance formula and our variables, we can find the distance between the two points:

[tex]\displaystyle\huge\begin{aligned}d & = \sqrt{(1 - 7)^2 + (7 - 0)^2} \\& = \sqrt{(-6)^2 + (7)^2} \\& = \sqrt{36 + 49} \\& = \math\boxed{\sqrt{85}} \\\end{aligned}[/tex]

∴ since the radical is already in its simplest form, our distance between the two points is equal to √85.

Hope this helps!

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