Answered

Explore Westonci.ca, the premier Q&A site that helps you find precise answers to your questions, no matter the topic. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.

What are the coordinates of vertex D?

1. A(-5, -1), B(1, -1), and C(1, -5) are three vertices of rectangle ABCD.

2. A(-1, 4), B(7, 4), and C(7, -1) are three vertices of rectangle ABCD.

3. A(2, 3), B(7, 3), and C(7, -2) are three vertices of square ABCD.

4. A(2, 5), B(6, 5), and C(6, 1) are three vertices of square ABCD.

Possible coordinate options:
(-1, -1)

Sagot :

GinnyAnswer
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)
Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.