Answer: Part A: Rule for Translating a Point 4 Units Left and 8 Units Up
When a point is translated 4 units to the left and 8 units up, the rule for this translation can be expressed as follows:
To translate a point (x, y) 4 units to the left, subtract 4 from the x-coordinate.
To translate a point (x, y) 8 units up, add 8 to the y-coordinate.
Therefore, the rule for translating a point 4 units to the left and 8 units up is:
New x-coordinate = Old x-coordinate - 4
New y-coordinate = Old y-coordinate + 8
Part B: Location of Point A After Translation
Given that point A has coordinates (7,5), after applying the translation rule:
New x-coordinate of A = 7 - 4 = 3
New y-coordinate of A = 5 + 8 = 13
Therefore, after the translation, point A is located at (3,13).
Part C: Rule for Reflecting a Point Over the Y-Axis
When reflecting a point over the y-axis, the x-coordinate changes sign while the y-coordinate remains unchanged. The rule for reflecting a point (x, y) over the y-axis is:
New x-coordinate = - Old x-coordinate
New y-coordinate = Old y-coordinate
Part D: Coordinates of Point A After Reflection
Given that after translation point A was at (3,13), when reflected over the y-axis:
New x-coordinate of A = -3
New y-coordinate of A = 13
Therefore, after reflection over the y-axis, point A is located at (-3,13).
Part E: Congruence of Final Figure to Original Figure
Step-by-step explanation:
