Question

multiple-choice question a translation of (x - 3, y + 4) means shifting 3 units to the right and 4 units up shifting the figure 3 units down and 4 units to the right shifting 3 units to the left and 4 units up

Explanation:

To determine the translation of \((x - 3,y + 4)\), we use the rules for horizontal and vertical translations of a point \((x,y)\):

• For horizontal translation: If we have \((x - h)\), the graph shifts \(h\) units to the right (when \(h>0\)). Here, \(h = 3\), so the \(x\)-coordinate change (\(x-3\)) means a shift of 3 units to the right.
• For vertical translation: If we have \((y + k)\), the graph shifts \(k\) units up (when \(k>0\)). Here, \(k = 4\), so the \(y\)-coordinate change (\(y + 4\)) means a shift of 4 units up.

So the translation \((x - 3,y + 4)\) corresponds to shifting 3 units to the right and 4 units up.

Answer:

The correct option (assuming the first option is "shifting 3 units to the right and 4 units up") is: shifting 3 units to the right and 4 units up