Answered

Find solutions to your problems with the help of IDNLearn.com's knowledgeable users. Join our interactive Q&A platform to receive prompt and accurate responses from experienced professionals in various fields.

Given the vertices A(-1, 4), B(7, 4), and C(7, -1) of rectangle ABCD, determine the coordinates of vertex D.

Given the vertices A(-5, -1), B(1, -1), and C(1, -5) of rectangle ABCD, determine the coordinates of vertex D.

Given the vertices A(2, 3), B(7, 3), and C(7, -2) of square ABCD, determine the coordinates of vertex D.

Given the vertices A(2, 5), B(6, 5), and C(6, 1) of square ABCD, determine the coordinates of vertex D.

Sagot :

GinnyAnsweridn
Certainly! Let's find the coordinates of the fourth vertex [tex]\( D \)[/tex] for each of the given problems.

### Problem 1
Given vertices [tex]\( A(-1, 4) \)[/tex], [tex]\( B(7, 4) \)[/tex], and [tex]\( C(7, -1) \)[/tex]:

To find vertex [tex]\( D \)[/tex]:
- The x-coordinate of [tex]\( D \)[/tex] would be [tex]\( A_x + C_x - B_x = -1 + 7 - 7 = -1 \)[/tex].
- The y-coordinate of [tex]\( D \)[/tex] would be [tex]\( A_y + C_y - B_y = 4 + (-1) - 4 = -1 \)[/tex].

Therefore, the coordinates of vertex [tex]\( D \)[/tex] are [tex]\( (-1, -1) \)[/tex].

### Problem 2
Given vertices [tex]\( A(-5, -1) \)[/tex], [tex]\( B(1, -1) \)[/tex], and [tex]\( C(1, -5) \)[/tex]:

To find vertex [tex]\( D \)[/tex]:
- The x-coordinate of [tex]\( D \)[/tex] would be [tex]\( A_x + C_x - B_x = -5 + 1 - 1 = -5 \)[/tex].
- The y-coordinate of [tex]\( D \)[/tex] would be [tex]\( A_y + C_y - B_y = -1 + (-5) - (-1) = -5 \)[/tex].

Therefore, the coordinates of vertex [tex]\( D \)[/tex] are [tex]\( (-5, -5) \)[/tex].

### Problem 3
Given vertices [tex]\( A(2, 3) \)[/tex], [tex]\( B(7, 3) \)[/tex], and [tex]\( C(7, -2) \)[/tex]:

To find vertex [tex]\( D \)[/tex]:
- The x-coordinate of [tex]\( D \)[/tex] would be [tex]\( A_x + C_x - B_x = 2 + 7 - 7 = 2 \)[/tex].
- The y-coordinate of [tex]\( D \)[/tex] would be [tex]\( A_y + C_y - B_y = 3 + (-2) - 3 = -2 \)[/tex].

Therefore, the coordinates of vertex [tex]\( D \)[/tex] are [tex]\( (2, -2) \)[/tex].

### Problem 4
Given vertices [tex]\( A(2, 5) \)[/tex], [tex]\( B(6, 5) \)[/tex], and [tex]\( C(6, 1) \)[/tex]:

To find vertex [tex]\( D \)[/tex]:
- The x-coordinate of [tex]\( D \)[/tex] would be [tex]\( A_x + C_x - B_x = 2 + 6 - 6 = 2 \)[/tex].
- The y-coordinate of [tex]\( D \)[/tex] would be [tex]\( A_y + C_y - B_y = 5 + 1 - 5 = 1 \)[/tex].

Therefore, the coordinates of vertex [tex]\( D \)[/tex] are [tex]\( (2, 1) \)[/tex].

### Summary
- For the first rectangle: [tex]\( D = (-1, -1) \)[/tex].
- For the second rectangle: [tex]\( D = (-5, -5) \)[/tex].
- For the third square: [tex]\( D = (2, -2) \)[/tex].
- For the fourth square: [tex]\( D = (2, 1) \)[/tex].

These steps ensure that the fourth vertex [tex]\( D \)[/tex] is calculated correctly based on the given vertices of the rectangles and squares.
Thank you for using this platform to share and learn. Keep asking and answering. We appreciate every contribution you make. Accurate answers are just a click away at IDNLearn.com. Thanks for stopping by, and come back for more reliable solutions.