Let's solve this step by step for each case.
1. Given A(-5, -1), B(1, -1), and C(1, -5), find the coordinates of vertex D
In a rectangle or square, vertices A, B, C, and D form a closed figure such that both pairs of opposite sides are equal in length and parallel.
- The fourth vertex, D, should have coordinates that complete the rectangle.
- Based on the given vertices:
- Side AB runs horizontally from (-5, -1) to (1, -1).
- Side BC runs vertically from (1, -1) to (1, -5).
To complete the rectangle ABCD:
- D must share the x-coordinate of A and the y-coordinate of C.
Thus, the coordinates of D will be:
- [tex]\(D = (-5, -5)\)[/tex]
2. Given A(-1, 4), B(7, 4), and C(7, -1), find the coordinates of vertex D
- The fourth vertex D must complete the rectangle with A.
- Considering the coordinates:
- Side AB runs horizontally from (-1, 4) to (7, 4).
- Side BC runs vertically from (7, 4) to (7, -1).
To complete the rectangle ABCD:
- D must share the x-coordinate of A and the y-coordinate of C.
Thus, the coordinates of D will be:
- [tex]\(D = (-1, -1)\)[/tex]
3. Given A(2, 3), B(7, 3), and C(7, -2), find the coordinates of vertex D
- The fourth vertex D must complete the square with A.
- Considering the coordinates:
- Side AB runs horizontally from (2, 3) to (7, 3).
- Side BC runs vertically from (7, 3) to (7, -2).
To complete the square ABCD:
- D must share the x-coordinate of A and the y-coordinate of C.
Thus, the coordinates of D will be:
- [tex]\(D = (2, -2)\)[/tex]
4. Given A(2, 5), B(6, 5), and C(6, 1), find the coordinates of vertex D
- The fourth vertex D must complete the square with A.
- Considering the coordinates:
- Side AB runs horizontally from (2, 5) to (6, 5).
- Side BC runs vertically from (6, 5) to (6, 1).
To complete the square ABCD:
- D must share the x-coordinate of A and the y-coordinate of C.
Thus, the coordinates of D will be:
- [tex]\(D = (2, 1)\)[/tex]
In summary, the coordinates of the fourth vertices D are:
1. (-5, -5)
2. (-1, -1)
3. (2, -2)
4. (2, 1)
