Question

#1: what is the distance between point m and point n? *

Explanation:

Step1: Determine the coordinates of points M and N

From the graph, the coordinates of point \( M\) are \((-2,5)\) and the coordinates of point \( N\) are \((4,5)\)

Step2: Use the distance formula for points with the same y - coordinate

The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Since \(y_1 = y_2=5\), the formula simplifies to \(d=\vert x_2 - x_1\vert\)
Substitute \(x_1=-2\) and \(x_2 = 4\) into \(d=\vert x_2 - x_1\vert\), we get \(d=\vert4-(-2)\vert=\vert4 + 2\vert\)

Step3: Calculate the absolute value

\(\vert4 + 2\vert=\vert6\vert=6\)

Answer:

\(6\)