Question

What is the length of stack M N with bar on top ? Round to the nearest tenth of a unit.


units

Line segment on a coordinate grid. Segment begins at point M, whose coordinates are two, negative two, and ends at point N, whose coordinates are eight, four.

Answer 1

https://static.k12.com/calms_media/media/1578500_1579000/1578500/1/88da3ceb29f9eed33d82d83b001cab74fc012268/MS_IMC-150122-130504.jpg

Answer 2

hint:
we have to do this computation:
\[\begin{gathered}
L = \sqrt {{{\left( {{x_N} - {x_M}} \right)}^2} + {{\left( {{y_N} - {y_M}} \right)}^2}} = \hfill \\
\hfill \\
= \sqrt {{{\left( {8 - 2} \right)}^2} + {{\left( {4 - \left( { - 2} \right)} \right)}^2}} = ...? \hfill \\
\end{gathered} \]

Answer 3

uh.

Answer 4

such formula comes from the direct application of the Pythagorean Theorem

Answer 5

here are the next steps:
\[\begin{gathered}
\overline {MN} = \sqrt {{{\left( {{x_N} - {x_M}} \right)}^2} + {{\left( {{y_N} - {y_M}} \right)}^2}} = \hfill \\
\hfill \\
= \sqrt {{{\left( {8 - 2} \right)}^2} + {{\left( {4 - \left( { - 2} \right)} \right)}^2}} = \hfill \\
\hfill \\
= \sqrt {{6^2} + {{\left( {4 + 2} \right)}^2}} = \sqrt {{6^2} + {6^2}} = \hfill \\
\hfill \\
= \sqrt {36 + 36} = \sqrt {72} = ...? \hfill \\
\end{gathered} \]

Answer 6

so, what is the square root of 72?

Answer 7

https://www.algebra.com/cgi-bin/plot-formula.mpl?expression=6%2Asqrt%282%29&x=0003

Answer 8

Can you write it for me?

Answer 9

yes! It is correct, nevertheless, the exercise asks for a decimal number rounded to the nearest tenth
Now, we have:
\[6\sqrt 2 = 8.48528...\]
please round that number to the nearest tenth

Answer 10

8.4

Answer 11

better is \(8.5\) since the secon decimal figure is \(8\) which is greater than \(5\)

Answer 12

second*