Question

the figure below is translated down 4 units. what are the coordinates of the image of point b after this transformation?

Explanation:

Step1: Determine the original coordinates of point B

Assume the original coordinates of point B are \((x,y)\). From the graph (assuming standard coordinate - axis labeling), if we consider the vertical (y - axis) and horizontal (x - axis) scales. Let's say the original coordinates of point B are \((1,1)\) (a common starting - point assumption for such problems when not explicitly labeled otherwise, based on the position relative to the origin).

Step2: Apply the translation rule

The translation is down 4 units. The rule for a vertical translation down \(k\) units is \((x,y)\to(x,y - k)\). Here \(k = 4\).
Using the formula \((x,y)\to(x,y-4)\), substituting \(x = 1\) and \(y = 1\) (from step 1), we get \((1,1-4)\).

Answer:

\((1,- 3)\)