Question

part b
list the coordinates of the vertices of the rotated rectangle.
enter the correct coordinates in the boxes.

show hints

(□,□), (□,□), (□,□), (□,□)

Explanation:

Step1: Identify the rotated rectangle's vertices

Looking at the graph, the rotated (right) rectangle has vertices at the following grid points:

• First vertex: x=1, y=5 (since it's 1 unit right on x - axis and 5 units up on y - axis)
• Second vertex: x=3, y=1 (3 units right, 1 unit up)
• Third vertex: x=5, y=2 (5 units right, 2 units up)
• Fourth vertex: x=3, y=6 (3 units right, 6 units up) Wait, no, let's re - check. Wait, the coordinates are determined by the x (horizontal) and y (vertical) positions. Let's list them correctly by looking at the grid:

Wait, the correct way is to find each point's (x,y) where x is the horizontal coordinate (positive to the right, negative to the left) and y is the vertical coordinate (positive up, negative down).

Looking at the rotated rectangle (the one on the right side of the graph):

1. The top - left (with the checkmark) is at (1, 5) (x = 1, y = 5)
2. The bottom - left is at (3, 1) (x = 3, y = 1)
3. The bottom - right is at (5, 2) (x = 5, y = 2)
4. The top - right is at (3, 6) (Wait, no, let's count the grid squares. Wait, maybe I made a mistake. Let's look again:

Wait, the four vertices of the rotated rectangle (the one on the right) are:

• (1, 5): x = 1, y = 5 (since it's 1 unit to the right of the origin on x - axis, 5 units up on y - axis)
• (3, 1): x = 3, y = 1 (3 units right, 1 unit up)
• (5, 2): x = 5, y = 2 (5 units right, 2 units up)
• (3, 6): x = 3, y = 6 (3 units right, 6 units up) Wait, no, when we connect these points, let's check the shape. Alternatively, maybe the correct coordinates are (1,5), (3,6), (5,2), (3,1). Let's verify the distance between (1,5) and (3,6): the horizontal distance is 3 - 1=2, vertical distance is 6 - 5 = 1. Between (3,6) and (5,2): horizontal distance 5 - 3 = 2, vertical distance 2 - 6=-4. Between (5,2) and (3,1): horizontal distance 3 - 5=-2, vertical distance 1 - 2=-1. Between (3,1) and (1,5): horizontal distance 1 - 3=-2, vertical distance 5 - 1 = 4. Wait, maybe a better way is to look at the grid:

Each vertex is at:

• (1, 5)
• (3, 6)
• (5, 2)
• (3, 1)

Wait, let's check the original (left) rectangle's vertices to see the rotation. The left rectangle has vertices at (-6,3), (-5,1), (-1,3), (-2,5)? No, wait the left rectangle: the check - marked point is (-6,3), then (-5,1), (-1,3), (-2,5). Then the rotated one: the check - marked point is (1,5), then (3,1), (5,2), (3,6). Wait, maybe I should list them as per the graph:

Looking at the right rectangle (rotated):

1. (1, 5)
2. (3, 6)
3. (5, 2)
4. (3, 1)

Wait, let's confirm the coordinates by looking at the x and y axes. For a point (x,y), x is the horizontal value (column) and y is the vertical value (row). So:

• The top - left vertex of the rotated rectangle (with the checkmark) is at x = 1, y = 5, so (1, 5)
• The top - right vertex is at x = 3, y = 6, so (3, 6)
• The bottom - right vertex is at x = 5, y = 2, so (5, 2)
• The bottom - left vertex is at x = 3, y = 1, so (3, 1)

Answer:

\((1, 5)\), \((3, 6)\), \((5, 2)\), \((3, 1)\)