Question

1. reason the coordinate of point m on a number line is 11. if mn = 12, what are the possible coordinates for n on the number line?

Explanation:

Step1: Recall the distance formula on a number line

The distance between two points \( M \) and \( N \) on a number line is given by \( |N - M| \), where \( M \) and \( N \) are the coordinates of the points. We know that \( M = 11 \) and the distance \( MN=12 \), so we have the equation \( |N - 11|=12 \).

Step2: Solve the absolute - value equation

The absolute - value equation \( |x| = a \) (where \( a>0 \)) has two solutions: \( x = a \) or \( x=-a \).
For the equation \( |N - 11| = 12 \), we can split it into two cases:

• Case 1: \( N - 11=12 \)

To solve for \( N \), we add 11 to both sides of the equation. So, \( N=12 + 11=23 \).

• Case 2: \( N - 11=- 12 \)

To solve for \( N \), we add 11 to both sides of the equation. So, \( N=-12 + 11=-1 \).

Answer:

The possible coordinates for \( N \) are \(-1\) and \(23\).