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 \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).

Step2: Substitute the values

Here, \(x_1=-6,y_1 = - 7,x_2=-3,y_2=-7\). Substitute into the formula: \(d=\sqrt{(-3-(-6))^2+(-7 - (-7))^2}\).
Simplify the expressions inside the square - root:
\(-3-(-6)=-3 + 6=3\) and \(-7-(-7)=-7 + 7 = 0\). So \(d=\sqrt{3^2+0^2}\).

Step3: Calculate the distance

Since \(3^2 = 9\) and \(0^2=0\), then \(d=\sqrt{9+0}=\sqrt{9}\). And \(\sqrt{9}=3\).

Answer:

\(3\)