Question

given: c(-5, -4), d(-2, -7) find: cd

Explanation:

Step1: Recall 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, \(C(-5,-4)\) so \(x_1=-5,y_1 = - 4\) and \(D(-2,-7)\) so \(x_2=-2,y_2=-7\).

Step2: Substitute values into formula

Substitute \(x_1=-5,y_1 = - 4,x_2=-2,y_2=-7\) into the formula:
\[

$$\begin{align*} CD&=\sqrt{(-2 - (-5))^2+(-7 - (-4))^2}\\ &=\sqrt{(-2 + 5)^2+(-7 + 4)^2}\\ &=\sqrt{(3)^2+(-3)^2}\\ &=\sqrt{9 + 9}\\ &=\sqrt{18}\\ &=\sqrt{9\times2}\\ &= 3\sqrt{2} \end{align*}$$

\]

Answer:

\(3\sqrt{2}\)