Question

in \\( \triangle k l m \\), the coordinates of the vertices are \\( k ( 5,5 ) \\). \\( l ( 6,2 ) \\). and \\( m ( 0,0 ) \\). what is the length of \\( \overline { l m } \\)? use the coordinate plant to find the length

Explanation:

Step1: Identify the coordinates

Given \( L(6,2) \) and \( M(0,0) \).

Step2: Use the distance formula

The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \( d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2} \).
Here \( x_1 = 6,y_1 = 2,x_2 = 0,y_2 = 0 \).
Substitute into the formula: \( d=\sqrt{(0 - 6)^2+(0 - 2)^2} \).

Step3: Calculate the squares

\((0 - 6)^2=(-6)^2 = 36\) and \((0 - 2)^2=(-2)^2 = 4\).
So \( d=\sqrt{36 + 4} \).

Step4: Sum and take square - root

\(36+4 = 40\), and \(d=\sqrt{40}\).
Simplify \(\sqrt{40}=\sqrt{4\times10}=2\sqrt{10}\approx 6.32\).

Answer:

The length of \(\overline{LM}\) is \(2\sqrt{10}\approx6.32\).