Question

given: d(-12, 10), e(-1, 5) find: de

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, \(x_1=- 12,y_1 = 10,x_2=-1,y_2 = 5\).

Step2: Substitute values into formula

First, calculate \(x_2 - x_1=-1-(-12)=-1 + 12 = 11\) and \(y_2 - y_1=5 - 10=-5\).
Then, substitute into the formula: \(DE=\sqrt{(11)^2+(-5)^2}\).

Step3: Simplify the expression

Calculate \((11)^2 = 121\) and \((-5)^2=25\). Then \(121 + 25=146\). So \(DE=\sqrt{146}\).

Answer:

\(\sqrt{146}\)