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35 votes
Find the distance between each pair of points. Round your answer to the nearest tenth, if necessary. Hint: Use the Pythagorean Theorem

Find the distance between each pair of points. Round your answer to the nearest tenth-example-1
User Alex Reynolds
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3.0k points

1 Answer

19 votes
19 votes

The distance between two points on the plane is given by the formula below


\begin{gathered} A=(x_1,y_1),B=(x_2,y_2) \\ \Rightarrow d(A,B)=\sqrt[]{(x_1-x_2)^2+(y_1-y_2)^2} \end{gathered}

Therefore, in our case,


A=(-1,-3),B=(5,2)

Thus,


\begin{gathered} \Rightarrow d(A,B)=\sqrt[]{(-1-5)^2+(-3-2)^2}=\sqrt[]{6^2+5^2}=\sqrt[]{36+25}=\sqrt[]{61} \\ \Rightarrow d(A,B)=\sqrt[]{61} \end{gathered}

Therefore, the answer is sqrt(61)

In general,


-(-n)=n

Remember that


-n=(-1)\cdot n

Therefore,


\begin{gathered} a-(-n)=a+(-1)(-n)=a+(-1)(-1\cdot n)=a+(-1)^2\cdot n=a+1\cdot n=a+n \\ \Rightarrow a-(-n)=a+n \end{gathered}

User Johannes Stein
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3.5k points