Question

calculate the distance between the points ( f=(1,-5) ) and ( l=(9,-2) ) in the coordinate plane. give an exact answer (not a decimal approximation).

Explanation:

Step1: Identify the coordinates

Let \(F=(x_1,y_1)=(1, - 5)\) and \(L=(x_2,y_2)=(9,-2)\)

Step2: Use the distance formula

The distance formula is \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)
Substitute the values: \(x_2 - x_1=9 - 1 = 8\), \(y_2 - y_1=-2-(-5)=-2 + 5=3\)
Then \(d=\sqrt{8^2+3^2}=\sqrt{64 + 9}=\sqrt{73}\)

Answer:

\(\sqrt{73}\)