Question

find the distance between the points (9, -6) and (-4, 7).
a) 2√85
b) 3√39
c) 13√2
d) 3√39

Explanation:

Step1: Identify the coordinates

Let \((x_1,y_1)=(9, - 6)\) and \((x_2,y_2)=(-4,7)\)

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

Substitute the values: \(x_2 - x_1=-4 - 9=-13\), \(y_2 - y_1=7-(-6)=13\)

Step3: Calculate the distance

\(d=\sqrt{(-13)^2 + 13^2}=\sqrt{169+169}=\sqrt{338}=\sqrt{2\times169}=13\sqrt{2}\)

Answer:

C. \(13\sqrt{2}\)