Question

what is the distance between points (6,4) & (-5, -1)?
√10
√√26
√130
√146

Explanation:

Step1: Identify the coordinates

Let \((x_1,y_1)=(6,4)\) and \((x_2,y_2)=(-5,-1)\)

Step2: Use the distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)

Substitute the values: \(d=\sqrt{(-5 - 6)^2+(-1 - 4)^2}\)

Step3: Simplify the expressions inside the square root

\(-5-6=-11\), \(-1 - 4=-5\)
\(d=\sqrt{(-11)^2+(-5)^2}=\sqrt{121 + 25}\)

Step4: Calculate the sum inside the square root

\(121+25 = 146\)
\(d=\sqrt{146}\)

Answer:

\(\sqrt{146}\)