Question

calculate the distance between the points ( m = (-8, 3) ) and ( q = (-1, 9) ) in the coordinate plane. give an exact answer (not a decimal approximation).

Explanation:

Step1: Identify the coordinates

Let \(M(x_1,y_1)=(-8,3)\) and \(Q(x_2,y_2)=(-1,9)\)

Step2: Use the distance formula

The distance formula is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)
Substitute the values: \(x_2 - x_1=-1-(-8)=7\), \(y_2 - y_1=9 - 3 = 6\)
So \(d=\sqrt{7^2+6^2}\)

Step3: Calculate the squares and sum

\(7^2 = 49\), \(6^2=36\), \(49 + 36=85\)
So \(d=\sqrt{85}\)

Answer:

\(\sqrt{85}\)