Question

question
what is the length of segment \\( \overline { c d } \\) in the figure below?
standard(s)
ncb 8.8. apply the pythagorean theorem to find the distance between two points in a coordinate system.
other questions on this standard 1 3

Explanation:

Step1: Determine the horizontal and vertical distances

From the graph, the horizontal distance between \(C\) and \(D\) (let's call it \(a\)) is \(4 - (- 2)=6\) units. The vertical distance between \(C\) and \(D\) (let's call it \(b\)) is \(4 - 1 = 3\) units.

Step2: Apply the Pythagorean theorem

The length of \(\overline{CD}\) (let's call it \(c\)) can be found using the Pythagorean theorem \(c=\sqrt{a^{2}+b^{2}}\). Substitute \(a = 6\) and \(b=3\) into the formula: \(c=\sqrt{6^{2}+3^{2}}=\sqrt{36 + 9}=\sqrt{45}\). Simplify \(\sqrt{45}=\sqrt{9\times5}=3\sqrt{5}\)

Answer:

\(3\sqrt{5}\)