Question

plot the image of point p under a translation by 5 units to the right and 7 units down.

Explanation:

Step1: Determine the coordinates of point \( P \)

From the graph, the coordinates of point \( P \) are \( (-1,5) \).

Step2: Apply the translation rule

The translation rule for moving \( 5 \) units to the right (add \( 5 \) to the \( x \)-coordinate) and \( 7 \) units down (subtract \( 7 \) from the \( y \)-coordinate) is \( (x,y)\to(x + 5,y-7) \).
Substitute \( x=-1 \) and \( y = 5 \) into the rule:
For the \( x \)-coordinate: \( x+5=-1 + 5=4 \)
For the \( y \)-coordinate: \( y - 7=5-7=-2 \)

Answer:

The image of point \( P(-1,5) \) after the translation is \( (4,-2) \). Plot the point \( (4,-2) \) on the coordinate - plane.