Question

1. select all transformations that take figure f to figure f. a. reflect figure f across the x - axis. b. reflect figure f across the y - axis. c. rotate figure f 90° clockwise around the origin. d. rotate figure f 180° degrees counterclockwise around the origin. e. translate figure f so that (4, 1) goes to (4, - 1). f. translate figure f so that (1, 4) goes to (1, - 1).

Explanation:

Step1: Recall transformation rules

• Reflection across x - axis: $(x,y)\to(x, - y)$.
• Reflection across y - axis: $(x,y)\to(-x,y)$.
• Rotation 90° clockwise around origin: $(x,y)\to(y,-x)$.
• Rotation 180° counter - clockwise around origin: $(x,y)\to(-x,-y)$.
• Translation: changes position by adding or subtracting values from coordinates.

Step2: Analyze each option

• Option A: Reflecting figure F across the x - axis changes the sign of the y - coordinates of all points on F. For example, a point $(x,y)$ on F becomes $(x, - y)$. This will take figure F to figure F'.
• Option B: Reflecting across the y - axis changes the sign of the x - coordinates. This will not take F to F'.
• Option C: Rotating 90° clockwise will not result in F'.
• Option D: Rotating 180° counter - clockwise will not result in F'.
• Option E: Translating so that $(4,1)$ goes to $(4, - 1)$ is equivalent to a reflection across the x - axis for the whole figure, which will take F to F'.
• Option F: Translating $(1,4)$ to $(1, - 1)$ is a vertical translation of 5 units down, which will not take F to F'.

Answer:

A. Reflect figure F across the x - axis.
E. Translate figure F so that $(4,1)$ goes to $(4, - 1)$.