Point A is translated to point B. Write the coordinates of both points. What do you notice?

Here are the solutions to the problems from the image: • Point A is translated to point B. Step 1: Identify the coordinates of point A and point B from the grid. Point A is at (2,3). Point B is at (6,2). Step 2: Write the coordinates and describe the translation. Coordinates of point A: (2,3) Coordinates of point B: (6,2) To get from A to B, the x-coordinate changes from 2 to 6 (an increase of 4), and the y-coordinate changes from 3 to 2 (a decrease of 1). What you notice: The point has been translated 4 units to the right and 1 unit down. The x-coordinate increased by 4, and the y-coordinate decreased by 1. The coordinates are A=(2,3), B=(6,2)*. What you notice: The x-coordinate increased by 4, and the y-coordinate decreased by 1.*. • Point C is translated to point D. Step 1: Identify the coordinates of point C and point D from the grid. Point C is at (3,3). Point D is at (3,1). Step 2: Write the coordinates and describe the translation. Coordinates of point C: (3,3) Coordinates of point D: (3,1) To get from C to D, the x-coordinate remains the same (3), and the y-coordinate changes from 3 to 1 (a decrease of 2). What you notice: The point has been translated 2 units down. The x-coordinate stayed the same, and the y-coordinate decreased by 2. The coordinates are C=(3,3), D=(3,1)*. What you notice: The x-coordinate stayed the same, and the y-coordinate decreased by 2.*. • Teddy plots a point that has the coordinates (5, 4). He translates the point so that it has the same x-coordinate, but a different y-coordinate. Has he translated the point up/down or left/right? Step 1: Analyze the effect of the translation on the coordinates. If the x-coordinate remains the same, the point has not moved horizontally (left or right). If the y-coordinate changes, the point has moved vertically (up or down). Step 2: Conclude the direction of translation. Since the x-coordinate is the same and the y-coordinate is different, Teddy has translated the point up/down. He has translated the point up/down*. • The point is translated 4 squares to the right and 2 squares down. Step 1: Identify the initial coordinates of the point from the grid. The initial point is at (4,2). Step 2: Apply the translation to find the new coordinates. Translate 4 squares to the right: add 4 to the x-coordinate. Translate 2 squares down: subtract 2 from the y-coordinate. New x-coordinate: 4+4 = 8 New y-coordinate: 2-2 = 0 The new coordinates are (8,0). Step 3: Write the coordinates and describe what you notice. Initial coordinates: (4,2) New coordinates: (8,0) What you notice: The x-coordinate increased by 4, and the y-coordinate decreased by 2. The coordinates are Initial=(4,2), New=(8,0)*. What you notice: The x-coordinate increased by 4, and the y-coordinate decreased by 2.*. • Complete the table. Step 1: Fill in the missing "Translation" for the second row. Original coordinates: (5,2) New coordinates: (2,5) Change in x: 2-5 = -3 (3 left) Change in y: 5-2 = 3 (3 up) Translation: 3 left and 3 up. Step 2: Fill in the missing "New coordinates" for the third row. Original coordinates: (6,7) Translation: 1 left and 1 down New x-coordinate: 6-1 = 5 New y-coordinate: 7-1 = 6 New coordinates: (5,6). The completed table is: | Coordinates | Translation | New coordinates | | :---------- | :--------------- | :-------------- | | (1,3) | 2 right and 1 down | (3,2) | | (5,2) | 3 left and 3 up | (2,5) | | (6,7) | 1 left and 1 down | (5,6) | • A triangle is translated so that point A translates to point B. Step 1: Identify the coordinates of point A and point B. Point A is at (1,6). Point B is at (5,4). Step 2: Determine the translation vector from A to B. Change in x: 5-1 = 4 (4 units right) Change in y: 4-6 = -2 (2 units down) The translation is 4 units right and 2 units down. Step 3: Identify the coordinates of the other two vertices of the original triangle. Let's call the bottom-left vertex V_1 and the bottom-right vertex V_2. V_1 = (1,3) V_2 = (2,3) Step 4: Apply the translation to V_1 and V_2 to find the coordinates of the translated vertices. For V_1' = (1+4, 3-2) = (5,1) For V_2' = (2+4, 3-2) = (6,1) The coordinates of the other vertices of the translated triangle are (5,1) and (6,1). How did you work this out? I first found the translation vector by comparing the coordinates of point A (1,6) and its translated position B (5,4). The x-coordinate changed by 5-1=4 (4 units right), and the y-coordinate changed by 4-6=-2 (2 units down). Then, I identified the coordinates of the other two vertices of the original triangle, which are (1,3) and (2,3). Finally, I applied the same translation (4 units right, 2 units down) to each of these vertices to find their new coordinates: (1+4, 3-2) = (5,1) and (2+4, 3-2) = (6,1). 3 done, 2 left today. You're making progress.