Question

Can you find the distance between (5,10) and (8,10)?

Answer 1

the distance between (5,10) and (8,10) is 3.

Step-by-step explanation:

Here's the required formula to find distance between (5,10) and (8,10) :

`\implies{\small{\pmb{\sf{d = \sqrt{\Big(x_(2) - x_(1) \Big)^(2) + \Big(y_(2) - y_(1) \Big)^(2)}}}}}`

Here, we have provided :

`\begin{gathered}\begin{gathered} \footnotesize\rm {\underline{\underline{Where}}}\begin{cases}& \sf x_2 = 8\\ & \sf x_1 = 5\\ & \sf y_2 = 10\\& \sf y_1 = 10\end{cases} \end{gathered}\end{gathered}`

Substituting all the given values in the formula to find the distance between (5,10) and (8,10):

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

`\implies{\small{\sf{d = \sqrt{\Big(8 - 5 \Big)^(2) + \Big(10 - 10\Big)^(2)}}}}`

`\implies{\small{\sf{d = \sqrt{\Big( \: 3 \: \Big)^(2) + \Big( \: 0 \: \Big)^(2)}}}}`

`\implies{\small{\sf{d = √(\Big(3 * 3 \Big)+ \Big(0 * 0\Big))}}}`

`\implies{\small{\sf{d = √(\big( \: 9 \: \big)+ \big( \: 0 \: \big))}}}`

`\implies{\small{\sf{d = √(9 + 0)}}}`

`\implies{\small{\sf{d = √(9)}}}`

`\implies{\sf{\underline{\underline{\red{d = 3}}}}}`

Hence, the distance between (5,10) and (8,10) is 3.

`\rule{300}{2.5}`

Answer 2

3

Explanation:

The distance formula is:

`d = \sqrt {\left( {x_2 - x_1 } \right)^2 + \left( {y_2 - y_1 } \right)^2 }`

Now we can plug the coordinates into the equation

`d = \sqrt {\left({8 - 5 \right)^2 + \left( {10 - 10 } \right)^2 }`

Then we simplify

`d = \sqrt {\left 3 \right^2 + \left 0 \right^2 }`

`d=√(9+0)`

`d=√(9)`

`d=3`