Question

2. Find the distance between points (1,3) and (9,18) on the coordinate plane.

Show work

Answer 1

`d =\sqrt{(x2 - x1) ^(2) + (y2 - y1) ^(2) } \\ d = \sqrt{ {(9 - 1) }^(2) + {(18 - 3)}^(2) } \\ d = \sqrt{ {8}^(2) + 15 ^(2) } \\ d = √(64 + 225 ) \\ d = √(289) \\ d = 17`

Answer 2

The distance between points (1,3) and (9,18) is 17.

Step-by-step Step-by-step explanation:

Here's the required formula to find distance between points (1,3) and (9,18) :

`\star{\small{\underline{\boxed{\sf{Distance = \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 = 9\\ & \sf x_1 = 1\\ & \sf y_2 = 18\\& \sf y_1 = 3\end{cases} \end{gathered}\end{gathered}`

Substituting all the given values in the formula to find the distance between points (1,3) and (9,18) :

`\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(9 - 1\Big)^(2) + \Big(18 - 3\Big)^(2)}}}}`

`\implies{\small{\sf{d = \sqrt{\Big( \: 8 \: \Big)^(2) + \Big( \: 15 \: \Big)^(2)}}}}`

`\implies{\small{\sf{d = √(\Big( 8 * 8\Big) + \Big( 15 * 15\Big))}}}`

`\implies{\small{\sf{d = √(\big( \: 64 \: \big) + \big( \: 225 \: \big))}}}`

`\implies{\small{\sf{d = √(64 + 225)}}}`

`\implies{\small{\sf{d = √(289)}}}`

`\implies{\sf{\underline{\underline{\red{d = 17}}}}}`

Hence, the distance between points (1,3) and (9,18) is 17.

`\rule{300}{2.5}`