Question

given: e(11, -10), f(-4, -1) find: ef

Explanation:

Step1: Recall distance formula

The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).

Step2: Identify coordinates

For points \(E(11,-10)\) and \(F(-4,-1)\), we have \(x_1 = 11\), \(y_1=-10\), \(x_2=-4\), \(y_2 = -1\).

Step3: Substitute into formula

Substitute the values into the distance formula:
\[

$$\begin{align*} EF&=\sqrt{(-4 - 11)^2+(-1-(-10))^2}\\ &=\sqrt{(-15)^2+(9)^2}\\ &=\sqrt{225 + 81}\\ &=\sqrt{306}\\ &=\sqrt{9\times34}\\ &= 3\sqrt{34} \end{align*}$$

\]

Answer:

\(3\sqrt{34}\)