Question

unit 8: algebraic connections to geometry - copy
graphing calculator
find the length of ab given ( a(-5,3) ) and ( b(-2,-3) ).
express your answer in simplest radical form.
( 5sqrt{3} )
7
( sqrt{65} )
( 3sqrt{5} )

Explanation:

Step1: 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 \(x_1=-5,y_1 = 3,x_2=-2,y_2=-3\).

Step2: Substitute the values into the formula

\(AB=\sqrt{(-2-(-5))^2+(-3 - 3)^2}=\sqrt{(-2 + 5)^2+(-6)^2}\).

Step3: Simplify the expression inside the square - root

\(\sqrt{(3)^2+(-6)^2}=\sqrt{9 + 36}\).

Step4: Calculate the sum

\(\sqrt{45}\).

Step5: Simplify the radical

\(\sqrt{45}=\sqrt{9\times5}=3\sqrt{5}\).

Answer:

\(3\sqrt{5}\)