Question

For questions 1-2, find the distance and midpoint of the segments given the endpoints. 1. AB with A(3, 4) and B(-1, 10) Midpoint

Answer 1

Given the points A(3,4) and B(-1,10), we can find the distance between them using the following function:

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

then, we have the following:

`\begin{gathered} (x_1,y_1)=(3,4)=A \\ (x_2,y_2)=(-1,10)=B \\ \Rightarrow d(A,B)=\sqrt[]{(-1-3)^2+(10-4)^2}=\sqrt[]{4^2+6^2}=\sqrt[]{16+36}=\sqrt[]{52} \\ =\sqrt[]{4\cdot13}=2\cdot\sqrt[]{13} \\ d(A,B)=2\cdot\sqrt[]{13} \end{gathered}`