Question

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

Answer 1

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,

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