Question

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

Answer 1

Answer:

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

Step-by-step explanation:

Let's recall what the distance formula is:

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

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:

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

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

Hope this helps!

Answer 2

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✞︎ Solution ✞︎

➪ In order to calculate the required distance use the the distance formula

$\displaystyle{\implies\:\underline{\boxed{ \purple{\bf\:\bigg \lgroup\: \: d = \sqrt{(x_2 - x_1 {)}^{2} \: + \: ( y_2 - y_1 {)}^{2} \:} \: \bigg\rgroup} \: }}}$

❒ Where ❒

$\rm \longrightarrow (x_1 ,y_1) \: and \:(x_2,y_2)$ are 2 coordinate points.

❖ The 2 points given here are

• ➪ ( 1 , -7 )

and

• ➪ ( 7, 0 )

❖ Assume that ,❖

$\rm \longrightarrow (x_1 ,y_1) =( 1 ,-7) \: \\ \rm \: and \\ \rm\longrightarrow \:(x_2,y_2) = (7,0)$

$: : \rm \implies \: d = \sqrt{(7 -1 {)}^{2} + {(0 -( - 7)) }^{2} }$

$: : \rm \implies \: d = \sqrt{(6 {)}^{2} + {(7)}^{2} }$

$: : \rm \implies \: d = \sqrt{(36 {)} + {(49)}}$

$: : \bf \implies \: d = \sqrt{85} \longleftarrow \rm in \: radical \: form$

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