he point (4,1) is reflected in the y-axis. What are the coordinates of its image?(1 point)

Question

Responses

(−4,1)
open paren negative 4 comma 1 close paren - no response given

(4,−1)
open paren 4 comma negative 1 close paren - no response given

(−1,−4)
open paren negative 1 comma negative 4 close paren - no response given

(1,4)

Answer 1

When a point is reflected across the y-axis, the x-coordinate changes sign while the y-coordinate remains the same.

For the point (4, 1):

• The x-coordinate 4 becomes -4.
• The y-coordinate remains 1.

Therefore, the coordinates of the image after reflecting the point (4, 1) in the y-axis are (-4, 1).

So the correct response is:

(−4, 1)

Answer 2

When reflecting a figure across the y-axis, which coordinate(s) remain the same?(1 point)
Responses

x-coordinates
x -coordinates

inverse coordinates
inverse coordinates

y-coordinates
y -coordinates

polar coordinates

Answer 3

When reflecting a figure across the y-axis, the y-coordinates remain the same. Only the x-coordinates change sign.

Therefore, the correct response is:

y-coordinates

Answer 4

An image is drawn of a figure. After a 180° (counterclockwise) rotation about the origin, P(7,−2) is mapped to P′(−7,2) . Identify the rule that maps P to P′ .(1 point)
Responses

(x,y)→(x,−y)
left parenthesis x comma y right parenthesis right arrow left parenthesis x comma negative y right parenthesis

(x,y)→(−x,y)
left parenthesis x comma y right parenthesis right arrow left parenthesis negative x comma y right parenthesis

(x,y)→(y,x)
left parenthesis x comma y right parenthesis right arrow left parenthesis y comma x right parenthesis

(x,y)→(−x,−y)

Answer 5

A 180° (counterclockwise) rotation about the origin transforms any point (x, y) to (-x, -y).

For the point \( P(7, -2) \) after rotation, it is mapped to \( P′(-7, 2) \), which confirms the 180° rotation transformation rule.

Thus, the rule that maps \( P \) to \( P′ \) is:

(x, y) → (−x, −y)

Answer 6

The coordinates for a point and its image are Q(−3,−5) and Q′(5,−3) . Based on the mapping rules for rotations, which transformation occurred?(1 point)
Responses

a −90-degree (clockwise) rotation
a negative 90 -degree (clockwise) rotation

a 270-degree (counterclockwise) rotation
a 270-degree (counterclockwise) rotation

a −180-degree (clockwise) rotation or a 180-degree (counterclockwise) rotation
a negative 180 -degree (clockwise) rotation or a 180-degree (counterclockwise) rotation

a 90-degree (counterclockwise) rotation

Answer 7

To determine which transformation occurred from point \( Q(-3, -5) \) to point \( Q'(5, -3) \), we can analyze the coordinates based on the rules for rotation.

• A 90-degree counterclockwise rotation transforms \( (x, y) \) to \( (-y, x) \).
• A 90-degree clockwise rotation transforms \( (x, y) \) to \( (y, -x) \).
• A 180-degree rotation (either direction) transforms \( (x, y) \) to \( (-x, -y) \).

Let's apply a 90-degree clockwise rotation to \( Q(-3, -5) \):

1. Switch the coordinates: \( (-5, -3) \)
2. Change the sign of the new x-coordinate: \( (5, -3) \)

Now, this matches \( Q'(5, -3) \).

Therefore, based on the transformation that occurred, the correct response is:

a 90-degree (counterclockwise) rotation.

Answer 8

Identify the rotation function mapping used to turn A(−7,4) to A′(−4,−7) .(1 point)
Responses

(x,y)→(−x,−y)
left parenthesis x comma y right parenthesis right arrow left parenthesis negative x comma negative y right parenthesis

(x,y)→(−y,x)
left parenthesis x comma y right parenthesis right arrow left parenthesis negative y comma x right parenthesis

(x,y)→(y,−x)
left parenthesis x comma y right parenthesis right arrow left parenthesis y comma negative x right parenthesis

(x,y)→(−y,−x)

Answer 9

To determine the rotation function mapping used to turn point \( A(-7, 4) \) to point \( A'(-4, -7) \), we can examine the coordinates.

1. Starting point: A(-7, 4)
2. Ending point: A'(-4, -7)

If we consider the transformations that can occur through rotation:

• A 90-degree counterclockwise rotation transforms the coordinates \( (x, y) \) into \( (-y, x) \).
• A 90-degree clockwise rotation transforms the coordinates \( (x, y) \) into \( (y, -x) \).
• A 180-degree rotation transforms the coordinates \( (x, y) \) into \( (-x, -y) \).

Now, applying the possible transformations:

1. For a 90-degree counterclockwise rotation:

   • \( (-7, 4) \) → \( (-4, -7) \) (this matches \( A' \))

2. For a 90-degree clockwise rotation:

   • \( (-7, 4) \) → \( (4, 7) \) (not a match)

3. For a 180-degree rotation:

   • \( (-7, 4) \) → \( (7, -4) \) (not a match)

Since the mapping \( (x, y) \) results in \( (-y, x) \) leads us to \( A' \):

Thus, the rotation function mapping used is:

(x,y)→(−y,x).