Question

complete the reflection over y = x
(grid with points d, z, m, p and their reflection input boxes: d( , ), z( , ), m( , ), p( , ))

Explanation:

Step1: Find Coordinates of Original Points

First, determine the coordinates of points \( D \), \( Z \), \( M \), and \( P \) from the graph.

• Let's assume the grid has integer coordinates. From the graph:
• \( D \): Let's say \( D \) is at \( (4, 5) \) (since it's 4 units right on x - axis and 5 units up on y - axis).
• \( Z \): \( Z \) is at \( (3, 3) \) (3 units right on x - axis and 3 units up on y - axis).
• \( M \): \( M \) is at \( (3, 0) \) (3 units right on x - axis and 0 units on y - axis).
• \( P \): \( P \) is at \( (4, - 1) \) (4 units right on x - axis and 1 unit down on y - axis, so y - coordinate is - 1).

Step2: Apply Reflection over \( y = x \)

The rule for reflection over the line \( y=x \) is that if a point has coordinates \( (x,y) \), its image after reflection over \( y = x \) is \( (y,x) \).

• For point \( D(4,5) \):
• Using the rule \( (x,y)\to(y,x) \), the reflected point \( D' \) will have coordinates \( (5,4) \).
• For point \( Z(3,3) \):
• Since \( x = y=3 \), the reflected point \( Z' \) will be \( (3,3) \) (because swapping x and y gives the same point).
• For point \( M(3,0) \):
• Using the rule \( (x,y)\to(y,x) \), the reflected point \( M' \) will have coordinates \( (0,3) \).
• For point \( P(4, - 1) \):
• Using the rule \( (x,y)\to(y,x) \), the reflected point \( P' \) will have coordinates \( (-1,4) \).

Answer:

• \( D'(5,4) \)
• \( Z'(3,3) \)
• \( M'(0,3) \)
• \( P'(-1,4) \)