Question

# 14 iFind the distance between the points L(7,-1) and M(-2, 4). Answer in simplest exact form.The exact distance between the two points isPrevious1011 12 13 1415161718Next

Answer 1

Given:

The two points given are,

$L(7,-1),M(-2,4)$

Required:

To find the distance between two points.

Explanation:

Let the two points given be

$\begin{gathered} (x_1,y_1)=L(7,-1) \\ (x_2,y_2)=M(-2,4) \end{gathered}$

Then the distance (D) between two points is,

$\begin{gathered} D=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2} \\ \Rightarrow D=\sqrt{(-2-7)^2+(4+1)^2} \\ \Rightarrow D=\sqrt{(-9)^2+(5)^2} \\ \Rightarrow D=\sqrt{81+25} \\ \Rightarrow D=\sqrt{106} \\ \Rightarrow D=10.2956 \end{gathered}$

Final Answer:

The distance between two points is,

$D=10.2956$