Question

Find the distance between the two points.
A(0,1) and B( 6, 3.5)

Answer 1

AB = 6.5

Explanation:

If you use the distance formula, you can find the answer.

`\begin{array}{l}AB=√(\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2)\\=√(\left(6-0\right)^2+\left(3.5-1\right)^2)\\=√(6^2+2.5^2)\\=√(36+6.25)\\=√(42.25)\\AB=6.5\end{array}`

Therefore, the distance between the points A(0, 1) and B(6, 3.5) is 6.5. Hope this helps!

Answer 2

AB =
`{\boxed{\sf{6.5}}}`

Step-by-step explanation:

Here's the required formula to find distance between points :

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

As per given question we have provided that :

• 
  `x_2 = 6`
• 
  `x_1 = 0`
• 
  `y_2 = 3.5`
• 
  `y_1 = 1`

Substituting all the given values in the formula to find the distance between points A(0, 1) and B(6, 3.5) :

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

`{\implies{\small{\tt{AB = \sqrt{\Big(6 - 0 \Big)^(2) + \Big(3.5 - 1\Big)^(2)}}}}}`

`{\implies{\small{\tt{AB = \sqrt{\Big( \: 6 \: \Big)^(2) + \Big(2.5\Big)^(2)}}}}}`

`{\implies{\small{\tt{AB = √(\Big( 6 * 6 \Big)+ \Big(2.5 * 2.5\Big))}}}}`

`{\implies{\small{\tt{AB = √(\Big(36\Big)+ \Big(6.25\Big))}}}}`

`{\implies{\small{\tt{AB = √(\big(36 + 6.25\big))}}}}`

`{\implies{\small{\tt{AB = √(42.25)}}}}`

`{\implies{\small{\tt{AB =6.5}}}}`

Hence, the distance between points AB is 6.5

`\rule{300}{2.5}`