1) Write the translation that maps P(-4, 2) onto the point P ' (-1, -1)?

2) What are the coordinates of the reflection of the point (5,1) over the line y = x?

3) The coordinate notation for reflection over the y-axis is -?-.

4) If a translation has a coordinate notation of (x, y) -->(x + 1, y –3),
then what is the image of (5, -7)

5) (3, -4) is reflected over the y = 0, what is the image?

6)(3, -4) is reflected over the x = 2, what is the image?

7) If a translation has a coordinate notation of (x, y) à(x - 3, y + 5), then the figure will move

1) The translation that maps P(-4, 2) onto P'(-1, -1) is like moving a pimple from one side of your face to the other. You just have to shift everything 3 units to the right and 3 units down.

2) The reflection of the point (5, 1) over the line y = x is like looking in a mirror after eating a whole box of donuts. The x-coordinate becomes the y-coordinate and the y-coordinate becomes the x-coordinate, giving us the reflection (-1, 5).

3) The coordinate notation for reflection over the y-axis is like flipping your favorite book upside down. All you gotta do is change the sign of the x-coordinate. So if you have a point (x, y), the reflection over the y-axis is (-x, y). Easy peasy!

4) Using the translation (x, y) --> (x + 1, y - 3), the image of (5, -7) is like a mischievous monkey shaking things up. Move the point one unit to the right and three units down, and voila! The image is (6, -10).

5) When (3, -4) is reflected over the y = 0 line, it's like doing a handstand and seeing the world through your toes. The x-coordinate stays the same, but the y-coordinate changes sign. So the image is (3, 4).

6) When (3, -4) is reflected over the x = 2 line, it's like taking a leap of faith and landing on a trampoline. The x-coordinate becomes the reflection of the distance from the point to the line, so the image is (1, -4).

7) If a translation has a coordinate notation of (x, y) --> (x - 3, y + 5), then the figure will move like a partygoer who's had a few too many snacks. It will shift three units to the left and five units up. Get ready to dance!

1) To map point P(-4, 2) onto the point P'(-1, -1), we need to find the translation vector that shifts P to P'. We can do this by subtracting the coordinates of P from the coordinates of P':

Translation vector = P' - P
= (-1, -1) - (-4, 2)
= (-1 + 4, -1 - 2)
= (3, -3)

Therefore, the translation that maps P(-4, 2) onto P'(-1, -1) is (x, y) --> (x + 3, y - 3).

2) The line y = x is the line where the x-coordinates and y-coordinates are the same. To find the reflection of the point (5, 1) over this line, we need to switch the x and y coordinates.

Reflected point = (y, x)
= (1, 5)

Therefore, the reflection of the point (5, 1) over the line y = x is (1, 5).

3) The coordinate notation for reflection over the y-axis is (x, y) --> (-x, y). This means that the x-coordinate is negated while the y-coordinate remains the same.

4) To find the image of the point (5, -7) under the translation (x, y) --> (x + 1, y - 3), we simply apply the translation to the coordinates of the point.

Image = (5 + 1, -7 - 3)
= (6, -10)

Therefore, the image of the point (5, -7) under the translation (x, y) --> (x + 1, y - 3) is (6, -10).

5) When (3, -4) is reflected over the line y = 0 (the x-axis), the y-coordinate is negated while the x-coordinate remains the same.

Reflected image = (x, -y)
= (3, 4)

Therefore, the image of (3, -4) under the reflection over y = 0 is (3, 4).

6) When (3, -4) is reflected over the line x = 2, the x-coordinate becomes the difference between the line's equation (2) and x-coordinate (3), while the y-coordinate remains the same.

Reflected image = (2 - (x - 2), y)
= (4 - 3, -4)
= (1, -4)

Therefore, the image of (3, -4) under the reflection over x = 2 is (1, -4).

7) The figure will move in the direction opposite to the translation vector. In this case, the translation vector is (x, y) --> (x - 3, y + 5).

Therefore, the figure will move 3 units to the left and 5 units up.

1) To find the translation that maps P(-4, 2) onto P'(-1, -1), we need to determine the horizontal and vertical shift between the two points.

Horizontal shift:
The x-coordinate of P' is -1, while the x-coordinate of P is -4. To find the horizontal shift, we subtract the x-coordinate of P from the x-coordinate of P': -1 - (-4) = 3. Therefore, there is a horizontal shift of 3 units to the right.

Vertical shift:
The y-coordinate of P' is -1, while the y-coordinate of P is 2. To find the vertical shift, we subtract the y-coordinate of P from the y-coordinate of P': -1 - 2 = -3. Therefore, there is a vertical shift of 3 units downward.

So, the translation that maps P(-4, 2) onto P'(-1, -1) is (x, y) --> (x + 3, y - 3).

2) To find the coordinates of the reflection of the point (5, 1) over the line y = x, we need to find the line of reflection.

The line of reflection y = x is the diagonal line that passes through the points where x = y.

To reflect a point over a line, we need to find the perpendicular distance from the point to the line and then move the same distance in the opposite direction.

In this case, the point (5, 1) is already on the line y = x. So, its reflection will be the same as the original point.

Therefore, the coordinates of the reflection of the point (5, 1) over the line y = x are (5, 1).

3) The coordinate notation for reflection over the y-axis is (x, y) --> (-x, y). This means that the x-coordinate remains the same, but the y-coordinate is negated.

4) To find the image of the point (5, -7) under the given translation (x, y) --> (x + 1, y - 3), we apply the translation to the coordinates of the point.

The x-coordinate of the image is obtained by adding 1 to the x-coordinate of the original point: 5 + 1 = 6.
The y-coordinate of the image is obtained by subtracting 3 from the y-coordinate of the original point: -7 - 3 = -10.

Therefore, the image of the point (5, -7) under the given translation is (6, -10).

5) When a point (3, -4) is reflected over the line y = 0 (the x-axis), the y-coordinate is negated, while the x-coordinate remains the same.

So, the image of (3, -4) is (3, 4).

6) When a point (3, -4) is reflected over the line x = 2, the x-coordinate is negated, while the y-coordinate remains the same.

So, the image of (3, -4) is (-3, -4).

7) The given translation (x, y) --> (x - 3, y + 5) indicates that the figure will move 3 units to the left (negative x-direction) and 5 units upward (positive y-direction).

A(2,3) What is the A" coordinate?

Posting a whole homework assignment with no evidence of any attempt on your part will get you scant help here. Surely you have covered the relevant material, so you must have some ideas on at least some of the problems...

The hints I posted earlier should get you started on most of them. Evidently you just want someone to do all of your work for you.