Question

practice - radical equations and applications
18 points possible answered: 17/18
question 15
find the distance between the points (4,-4) and (-3,-1)
distance =

Explanation:

Step1: Identify 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, \(x_1 = 4,y_1=-4,x_2=-3,y_2 = -1\).

Step2: Calculate \(x_2 - x_1\) and \(y_2 - y_1\)

\(x_2 - x_1=-3 - 4=-7\), \(y_2 - y_1=-1-(-4)=-1 + 4 = 3\).

Step3: Substitute into the formula

\(d=\sqrt{(-7)^2+3^2}=\sqrt{49 + 9}=\sqrt{58}\).

Answer:

\(\sqrt{58}\)