Question

find the distance between the points (-5, 6) and (7, 6). distance:

Explanation:

Step1: Identify the coordinates

The two points are \((-5, 6)\) and \((7, 6)\). Here, the \(y\)-coordinates are the same (\(y_1 = y_2 = 6\)), so the distance between them is the absolute difference of the \(x\)-coordinates.

Step2: Calculate the distance

The formula for the distance between two points \((x_1,y_1)\) and \((x_2,y_2)\) when \(y_1 = y_2\) is \(d=\vert x_2 - x_1\vert\). Substituting \(x_1=-5\) and \(x_2 = 7\), we get \(d=\vert7-(-5)\vert=\vert7 + 5\vert=\vert12\vert = 12\).

Answer:

12