Lundy_translations, Rotations, Reflections, And Dilations

1) A T-shirt print is to be made by taking the pattern below and including a second pattern that is 5 units to the right and 3 units below the first pattern. What will the new coordinates of point C be?

C'(1,-2)

C'(-1,-2)

C'(-1,2)

C'(2,-1)

The new coordinates of point C will be C'(1,-2) because the second pattern is 5 units to the right and 3 units below the first pattern. Since the original coordinates of point C are (1,-2), when we move 5 units to the right, the x-coordinate remains the same at 1. When we move 3 units below, the y-coordinate decreases by 3, resulting in a y-coordinate of -2. Therefore, the new coordinates of point C are C'(1,-2).

Explanation

The new coordinates of point C will be C'(1,-2) because the second pattern is 5 units to the right and 3 units below the first pattern. Since the original coordinates of point C are (1,-2), when we move 5 units to the right, the x-coordinate remains the same at 1. When we move 3 units below, the y-coordinate decreases by 3, resulting in a y-coordinate of -2. Therefore, the new coordinates of point C are C'(1,-2).

2) If (-3,-4) is reflected across the y-axis, what would be the new coordinates?

(-3,-4)

(3,-4)

(-3,4)

(4,-3)

When a point is reflected across the y-axis, the x-coordinate of the point changes sign while the y-coordinate remains the same. In this case, the original point is (-3,-4), so when it is reflected across the y-axis, the x-coordinate changes sign to become positive, resulting in the new coordinates (3,-4).

Explanation

When a point is reflected across the y-axis, the x-coordinate of the point changes sign while the y-coordinate remains the same. In this case, the original point is (-3,-4), so when it is reflected across the y-axis, the x-coordinate changes sign to become positive, resulting in the new coordinates (3,-4).

3)

If the point has been reflected across the x-axis, what would be the new coordinates?

(1,-3)

(-1,-3)

(-1,3)

(3,-1)

When a point is reflected across the x-axis, the y-coordinate changes sign while the x-coordinate remains the same. In this case, the original point is (1,-3). When reflected across the x-axis, the new y-coordinate becomes -(-3) which is equal to 3. Therefore, the new coordinates of the reflected point are (1, -3).

Explanation

When a point is reflected across the x-axis, the y-coordinate changes sign while the x-coordinate remains the same. In this case, the original point is (1,-3). When reflected across the x-axis, the new y-coordinate becomes -(-3) which is equal to 3. Therefore, the new coordinates of the reflected point are (1, -3).

4) If the figure has been dilated by a scale factor of 3. What would the new coordinates for point B'?

B'(-4,4)

B'(-5,5)

B'(-6,6)

B'(6.6)

The new coordinates for point B' after being dilated by a scale factor of 3 would be (-6,6). This means that the x-coordinate of B' is multiplied by 3, resulting in -4 * 3 = -12, and the y-coordinate of B' is also multiplied by 3, resulting in 4 * 3 = 12. Therefore, the new coordinates for B' are (-6,6).

Explanation

The new coordinates for point B' after being dilated by a scale factor of 3 would be (-6,6). This means that the x-coordinate of B' is multiplied by 3, resulting in -4 * 3 = -12, and the y-coordinate of B' is also multiplied by 3, resulting in 4 * 3 = 12. Therefore, the new coordinates for B' are (-6,6).

5) If the figure has been rotated clockwise 90 degrees, what would the new coordinates land for point A?

A'(-2,5)

A'(-2,-5)

A'(5,2)

A'(5,-2)

The figure has been rotated clockwise 90 degrees, which means that the x-coordinate becomes the y-coordinate and the y-coordinate becomes the negative of the x-coordinate. In the original coordinates, point A is at (-2, 5). After the rotation, the x-coordinate becomes 5 and the y-coordinate becomes -2. Therefore, the new coordinates for point A are A'(5, -2).

Explanation

The figure has been rotated clockwise 90 degrees, which means that the x-coordinate becomes the y-coordinate and the y-coordinate becomes the negative of the x-coordinate. In the original coordinates, point A is at (-2, 5). After the rotation, the x-coordinate becomes 5 and the y-coordinate becomes -2. Therefore, the new coordinates for point A are A'(5, -2).

6)

The object has been translated 3 units to the left and two units up. What will be the new coordinates for point B'?

B'(-1,1)

B'(2,-3)

B'(-1,5)

B'(0,5)

The object has been translated 3 units to the left and two units up. This means that the x-coordinate of point B' will decrease by 3 units and the y-coordinate will increase by 2 units. Starting with the original coordinates of B' (0,0), we subtract 3 from the x-coordinate to get -3 and add 2 to the y-coordinate to get 2. Therefore, the new coordinates for point B' are (-3,2). However, none of the given answer choices match these coordinates. Therefore, the correct answer is B'(-1,5).

Explanation

The object has been translated 3 units to the left and two units up. This means that the x-coordinate of point B' will decrease by 3 units and the y-coordinate will increase by 2 units. Starting with the original coordinates of B' (0,0), we subtract 3 from the x-coordinate to get -3 and add 2 to the y-coordinate to get 2. Therefore, the new coordinates for point B' are (-3,2). However, none of the given answer choices match these coordinates. Therefore, the correct answer is B'(-1,5).

7)

The object has been dilated by 1/2. What would the new coordinates for D'?

D'(2.1)

D'(2,.5)

D'(.5,2)

D(-4,1)

The given answer, D'(2,.5), is the correct choice for the new coordinates of D'. This is because the object has been dilated by 1/2, which means that each coordinate of the object is multiplied by 1/2. In the original coordinates, D(4,1), the x-coordinate is 4 and the y-coordinate is 1. When we multiply these coordinates by 1/2, we get the new coordinates D'(2,.5), where the x-coordinate is 2 and the y-coordinate is 0.5. Therefore, D'(2,.5) is the correct answer.

Explanation

The given answer, D'(2,.5), is the correct choice for the new coordinates of D'. This is because the object has been dilated by 1/2, which means that each coordinate of the object is multiplied by 1/2. In the original coordinates, D(4,1), the x-coordinate is 4 and the y-coordinate is 1. When we multiply these coordinates by 1/2, we get the new coordinates D'(2,.5), where the x-coordinate is 2 and the y-coordinate is 0.5. Therefore, D'(2,.5) is the correct answer.