Question

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

Show work

Answer 1

Answer:

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

Answer 2

Answer:

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

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) :

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

$\implies{\small{\sf{d = \sqrt{\Big(9 - 1\Big)^{2} + \Big(18 - 3\Big)^{2}}}}}$

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

$\implies{\small{\sf{d = \sqrt{\Big( 8 \times 8\Big) + \Big( 15 \times 15\Big)}}}}$

$\implies{\small{\sf{d = \sqrt{\big( \: 64 \: \big) + \big( \: 225 \: \big)}}}}$

$\implies{\small{\sf{d = \sqrt{64 + 225}}}}$

$\implies{\small{\sf{d = \sqrt{289}}}}$

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

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

$\rule{300}{2.5}$