Question

What is the distance between points (5,2) and (1,-3) on a coordinate plane?A 3B 4.1C 8.5D 6.4

Answer 1

We are asked to find the distance between the following two points

`(5,2)\: and\: (1,-3)`

Recall that the distance formula is given by

`d=\sqrt[]{\mleft({x_2-x_1}\mright)^2+\mleft({y_2-y_1}\mright)^2}`
`\begin{gathered} \mleft(x_1,y_1\mright)=\mleft(5,2\mright) \\ (x_2,y_2_{})=(1,-3) \end{gathered}`

Let us substitute the given points into the above distance formula

`\begin{gathered} d=\sqrt[]{({x_2-x_1})^2+({y_2-y_1})^2} \\ d=\sqrt[]{({1_{}-5_{}})^2+({-3_{}-2})^2} \\ d=\sqrt[]{({-4})^2+({-5})^2} \\ d=\sqrt[]{16^{}+25^{}} \\ d=\sqrt[]{41} \\ d=6.4 \end{gathered}`

Therefore, the distance between the given two points is 6.4

Option D is the correct answer.