The following coordinate plane shows three of the vertices of a rectangle.

Question

On an 8 by 8 coordinate grid, T is plotted 1 unit right and 4 units up from the origin. P is plotted 6 units right and 2 units up from the origin. Z is plotted 3 units right and 5 units up from the origin.

(2 points)
What are the coordinates of Point Z? (
Choose
)

What are the coordinates of Point P? (
Choose
)

Which point has coordinates (1,4)?
Choose

In order to create a rectangle using these points as three of the vertices, what coordinates should be used for the fourth vertex? (
Choose
)

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Answer 1

Let's determine the coordinates for the points based on the information provided:

1. Coordinates of Point T:
   T is plotted 1 unit right and 4 units up from the origin (0,0). Therefore, the coordinates of Point T are (1, 4).

2. Coordinates of Point P:
   P is plotted 6 units right and 2 units up from the origin. Thus, the coordinates of Point P are (6, 2).

3. Coordinates of Point Z:
   Z is plotted 3 units right and 5 units up from the origin. Therefore, the coordinates of Point Z are (3, 5).

4. Which point has coordinates (1, 4):
   From our earlier deduction, Point T has the coordinates (1, 4).

5. To find the fourth vertex of the rectangle:
   Given points T(1, 4), P(6, 2), and Z(3, 5), we can denote the fourth vertex as V.

   • The x-coordinates of the opposite vertices will be paired:
     • (1, 4) and V have the same x-coordinate, which would imply that V has x=6.
     • (6, 2) and V have the same y-coordinate, which would imply that V has y=5.

   So the coordinates for the fourth vertex V would be (6, 5).

Summary of the answers:

• Coordinates of Point Z: (3, 5)
• Coordinates of Point P: (6, 2)
• Point with coordinates (1, 4): Point T
• Fourth vertex coordinates: (6, 5)