Question

using the distance formula from above find the distance between (-15,-18) and (18,-2). round to the nearest tenth.using the distance formula from above find the distance between (5,9) and (-7,-7). round to the nearest tenth.using the distance formula from above find the distance between (3,8) and (9,10). round to nearest tenth.

Answer 1

`\begin{gathered} 1.\text{ }d=36.7 \\ 2.\text{ }d=20 \\ 3.\text{ }d=6.3 \end{gathered}`

Step by step explanation:

The distance between two points is represented by the following expression:

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

1. Then, for (-15, -18) and (18, -2)

`\begin{gathered} d=\sqrt[]{(18-(-15))^2+(-2-(-18))^2} \\ d=\sqrt[]{(33)^2+(16)^2} \\ d=\sqrt[]{1089+256} \\ d=\sqrt[]{1345} \\ d\approx36.67 \\ \text{Rounding to the nearest tenth:} \\ d=36.7 \end{gathered}`

2. Now, for (5,9) and (-7,-7)

`\begin{gathered} d=\sqrt[]{(-7-5)^2+(-7-9)^2} \\ d=\sqrt[]{(-12)^2+(-16)^2} \\ d=\sqrt[]{144+256} \\ d=\sqrt[]{400} \\ d=20 \end{gathered}`

3. Finally, for (3,8) and (9,10)

`\begin{gathered} d=\sqrt[]{(9-3)^2+(10-8)^2} \\ d=\sqrt[]{6^2+2^2} \\ d=\sqrt[]{36+4} \\ d=\sqrt[]{40} \\ d=2\sqrt[]{10} \\ \text{Rounding to the nearest tenth:} \\ d=6.3 \end{gathered}`