To find the coordinates of point D to make a rectangle, we need to look at the positions of points A, B, and C. In a rectangle on a coordinate grid, opposite corners share either the same x-coordinate (vertical line) or the same y-coordinate (horizontal line).
Here is the step-by-step solution for each problem:
1)
* Point A is at $(2, 5)$. Point B is at $(6, 9)$. Point C is at $(6, 5)$.
* Point D must align vertically with A (x=2) and horizontally with B (y=9).
* Coordinates:
$(2, 9)$
2)
* Point A is at $(8, 2)$. Point B is at $(2, 2)$. The bottom-left corner is at $(2, 0)$.
* Point D is the bottom-right corner. It aligns vertically with A (x=8) and horizontally with the bottom-left corner (y=0).
* Coordinates:
$(8, 0)$
3)
* Point A is at $(4, 9)$. Point B is at $(2, 9)$. Point C is at $(2, 2)$.
* Point D must align vertically with A (x=4) and horizontally with C (y=2).
* Coordinates:
$(4, 2)$
4)
* Point A is at $(7, 4)$. Point B is at $(8, 4)$. Point C is at $(8, 2)$.
* Point D must align vertically with A (x=7) and horizontally with C (y=2).
* Coordinates:
$(7, 2)$
5)
* Point A is at $(2, 7)$. Point B is at $(2, 3)$. Point C is at $(6, 7)$.
* Point D must align vertically with C (x=6) and horizontally with B (y=3).
* Coordinates:
$(6, 3)$
6)
* Point A is at $(2, 7)$. Point B is at $(6, 7)$. Point C is at $(6, 1)$.
* Point D must align vertically with A (x=2) and horizontally with C (y=1).
* Coordinates:
$(2, 1)$
7)
* Point A is at $(9, 2)$. Point B is at $(2, 5)$. Point C is at $(9, 5)$.
* Point D must align vertically with B (x=2) and horizontally with A (y=2).
* Coordinates:
$(2, 2)$
8)
* Point A is at $(9, 8)$. Point B is at $(9, 6)$. Point C is at $(7, 6)$.
* Point D must align vertically with C (x=7) and horizontally with A (y=8).
* Coordinates:
$(7, 8)$
9)
* Point A is at $(1, 9)$. Point B is at $(7, 9)$. Point C is at $(7, 3)$.
* Point D must align vertically with A (x=1) and horizontally with C (y=3).
* Coordinates:
$(1, 3)$
10)
* Point A is at $(3, 4)$. Point B is at $(6, 4)$. Point C is at $(3, 1)$.
* Point D must align vertically with B (x=6) and horizontally with C (y=1).
* Coordinates:
$(6, 1)$
11)
* Point A is at $(6, 3)$. Point B is at $(6, 7)$. Point C is at $(3, 7)$.
* Point D must align vertically with C (x=3) and horizontally with A (y=3).
* Coordinates:
$(3, 3)$
Final Answer:
1. (2, 9)
2. (8, 0)
3. (4, 2)
4. (7, 2)
5. (6, 3)
6. (2, 1)
7. (2, 2)
8. (7, 8)
9. (1, 3)
10. (6, 1)
11. (3, 3)
Parent Tip: Review the logic above to help your child master the concept of 9th grade algebra worksheets.
