Question

find the distance between the points $(-6, -7)$ and $(3, -7)$.
distance:

Explanation:

Step1: Identify the formula

The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Here \(x_1=-6,y_1 = - 7,x_2=3,y_2=-7\).

Step2: Substitute the values

Substitute into the formula: \(d=\sqrt{(3-(-6))^2+(-7 - (-7))^2}=\sqrt{(3 + 6)^2+(0)^2}\).

Step3: Simplify the expression

First, calculate \(3+6 = 9\) and \(-7+7 = 0\). Then \(d=\sqrt{9^2+0^2}=\sqrt{81+0}=\sqrt{81}\).

Step4: Calculate the square - root

Since \(\sqrt{81}=9\).

Answer:

\(9\)