Question

given the following coordinates find the distance between them.
a: (7,4)
b: (-2,5)
√82
9
√65
√98

Explanation:

Step1: Identify the coordinates

Let \((x_1,y_1)=(7,4)\) and \((x_2,y_2)=(-2,5)\)

Step2: Use the distance formula

The distance formula is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)
Substitute the values: \(d=\sqrt{(-2 - 7)^2+(5 - 4)^2}\)

Step3: Simplify the expression

First, calculate \((-2 - 7)^2=(-9)^2 = 81\) and \((5 - 4)^2=1^2 = 1\)
Then \(d=\sqrt{81 + 1}=\sqrt{82}\)

Answer:

\(\sqrt{82}\)