Question
The vertices of a rectangle are located at (0, -1) , (0 2) , (-7,-1) , and (-7,2) . Each gridline on the coordinate plane represents one unit. Which coordinate plane correctly shows the rectangle?
A.
A rectangle on the coordinate plane has a vertex 1 unit up from the origin, another vertex 2 units down from the origin, another vertex 7 units to the left and 1 unit up from the origin, and another vertex 7 units to the left and 2 units down from the origin.
B.
A rectangle on the coordinate plane has a vertex 2 units up from the origin, another vertex 1 unit down from the origin, another vertex 7 units to the left and 2 units up from the origin, and another vertex 7 units to the left and 1 unit down from the origin.
C.
A rectangle on the coordinate plane has a vertex 2 units to the right of the origin, another vertex 1 unit to the left of the origin, another vertex 7 units down and 2 units to the right of the origin, and another vertex 7 units down and 1 unit to the left of the origin.
D.
A rectangle on the coordinate plane has a vertex 1 unit to the right of the origin, another vertex 2 units to the left of the origin, another vertex 7 units down and 1 unit to the right of the origin, and another vertex 7 units down and 2 units to the left of the origin.
A.
A rectangle on the coordinate plane has a vertex 1 unit up from the origin, another vertex 2 units down from the origin, another vertex 7 units to the left and 1 unit up from the origin, and another vertex 7 units to the left and 2 units down from the origin.
B.
A rectangle on the coordinate plane has a vertex 2 units up from the origin, another vertex 1 unit down from the origin, another vertex 7 units to the left and 2 units up from the origin, and another vertex 7 units to the left and 1 unit down from the origin.
C.
A rectangle on the coordinate plane has a vertex 2 units to the right of the origin, another vertex 1 unit to the left of the origin, another vertex 7 units down and 2 units to the right of the origin, and another vertex 7 units down and 1 unit to the left of the origin.
D.
A rectangle on the coordinate plane has a vertex 1 unit to the right of the origin, another vertex 2 units to the left of the origin, another vertex 7 units down and 1 unit to the right of the origin, and another vertex 7 units down and 2 units to the left of the origin.
Answers
GPT-4o mini
To determine which coordinate plane correctly shows the rectangle with vertices at (0, -1), (0, 2), (-7, -1), and (-7, 2), we first identify the locations of these vertices:
1. (0, -1) - This point is on the y-axis, 1 unit down from the origin.
2. (0, 2) - This point is also on the y-axis, 2 units up from the origin.
3. (-7, -1) - This point is 7 units left of the y-axis and 1 unit down from the origin.
4. (-7, 2) - This point is 7 units left of the y-axis and 2 units up from the origin.
Now, we can visualize the rectangle on the coordinate plane:
- The vertical sides of the rectangle are aligned along the x-coordinate of 0 and -7, and the horizontal sides are aligned along the y-coordinates of -1 and 2.
- In summary, the rectangle stretches from (0, -1) to (0, 2) vertically, and from (-7, -1) to (-7, 2) vertically as well.
Now, let's analyze the options given:
**A.** This describes a rectangle that is 1 unit up and 2 units down from the origin, and 7 units left with the same vertical coordinates. This does not match our coordinates.
**B.** This describes a rectangle that has a vertex 2 units up from the origin, which is (0, 2). It also mentions a vertex 1 unit down from the origin, which is (0, -1). The vertices at (-7, 2) and (-7, -1) matches as well, since it describes a vertex that is 7 units to the left with the respective vertical heights. This matches our rectangle.
**C.** This describes a rectangle that is 2 units to the right from the origin and doesn't match the coordinates we have.
**D.** This also does not match any of the points since the vertex placements seem incorrect.
Based on this analysis, the correct answer is:
**B.** A rectangle on the coordinate plane has a vertex 2 units up from the origin, another vertex 1 unit down from the origin, another vertex 7 units to the left and 2 units up from the origin, and another vertex 7 units to the left and 1 unit down from the origin.
1. (0, -1) - This point is on the y-axis, 1 unit down from the origin.
2. (0, 2) - This point is also on the y-axis, 2 units up from the origin.
3. (-7, -1) - This point is 7 units left of the y-axis and 1 unit down from the origin.
4. (-7, 2) - This point is 7 units left of the y-axis and 2 units up from the origin.
Now, we can visualize the rectangle on the coordinate plane:
- The vertical sides of the rectangle are aligned along the x-coordinate of 0 and -7, and the horizontal sides are aligned along the y-coordinates of -1 and 2.
- In summary, the rectangle stretches from (0, -1) to (0, 2) vertically, and from (-7, -1) to (-7, 2) vertically as well.
Now, let's analyze the options given:
**A.** This describes a rectangle that is 1 unit up and 2 units down from the origin, and 7 units left with the same vertical coordinates. This does not match our coordinates.
**B.** This describes a rectangle that has a vertex 2 units up from the origin, which is (0, 2). It also mentions a vertex 1 unit down from the origin, which is (0, -1). The vertices at (-7, 2) and (-7, -1) matches as well, since it describes a vertex that is 7 units to the left with the respective vertical heights. This matches our rectangle.
**C.** This describes a rectangle that is 2 units to the right from the origin and doesn't match the coordinates we have.
**D.** This also does not match any of the points since the vertex placements seem incorrect.
Based on this analysis, the correct answer is:
**B.** A rectangle on the coordinate plane has a vertex 2 units up from the origin, another vertex 1 unit down from the origin, another vertex 7 units to the left and 2 units up from the origin, and another vertex 7 units to the left and 1 unit down from the origin.