Question

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

Explanation:

Step1: Identify the coordinates

The coordinates of \(L\) are \((6,2)\) and of \(M\) are \((0,0)\).

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

Step4: Sum and simplify

\(36+4 = 40\), so \(d=\sqrt{40}\). Factor \(40\) as \(4\times10\), then \(d=\sqrt{4\times10}=2\sqrt{10}\approx6.32\).

Answer:

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