Laura is designing a rectangular porch for her house. On her scale drawing, the vertices of the rectangle are (2,7), (8,7), (2,9). What are the coordinates of the fourth vertex.
A. (8,9)
B. (7,9)
C. (7,2)
D. (2,8)
AAAaannndd the bot gets it wrong yet again!
No, (2,9) is already one of the vertices.
And besides, D = (2,8)
Note that AB is horizontal, with length 6
So CD also must have length 6.
So, pick A(8,9)
To find the coordinates of the fourth vertex of the rectangle, we can use the fact that opposite sides of a rectangle are parallel and of equal length.
Given the three vertices (2,7), (8,7), and (2,9), we can observe that the rectangle is horizontally oriented. This means that the fourth vertex should have the same y-coordinate as the third vertex (2,9), and a different x-coordinate.
Therefore, the coordinates of the fourth vertex are (8,9), which is option A.
To find the coordinates of the fourth vertex of the rectangle, you need to understand that a rectangle has opposite sides that are equal in length and parallel to each other.
Since the given vertices are (2,7), (8,7), and (2,9), we can determine the length of the sides of the rectangle.
The length of the rectangle can be calculated as the difference between the x-coordinates of two adjacent vertices:
Length = 8 - 2 = 6
Similarly, the width of the rectangle can be calculated as the difference between the y-coordinates of two adjacent vertices:
Width = 9 - 7 = 2
Now, let's analyze the options:
A. (8,9): If this were the fourth vertex, the length and width of the rectangle would not be equal since the length is 6 and the width is 2. Therefore, this is not the correct answer.
B. (7,9): If this were the fourth vertex, the length and width of the rectangle would still not be equal, as the length is still 6 and the width is still 2. So, this is not the correct answer either.
C. (7,2): If this were the fourth vertex, the length of the rectangle would be 7 - 2 = 5, which is not equal to the width of 2. Therefore, this is also not the correct answer.
D. (2,8): If this were the fourth vertex, the length of the rectangle would be 8 - 2 = 6, which is equal to the width. Hence, this is the correct answer.
Therefore, the coordinates of the fourth vertex are (2,8), which corresponds to option D.
We can start by using the fact that opposite sides of a rectangle are parallel and have the same length. Since the given sides have a length of 6 (from 2 to 8), we know that the missing side must also have a length of 6.
Looking at the given coordinates, we see that the two points on the top of the rectangle have the same y-coordinate of 7, while the point on the side has a y-coordinate of 9. Therefore, the missing point must also have a y-coordinate of 9.
To find the x-coordinate of the missing point, we can use the fact that opposite sides of a rectangle have the same x-coordinate. The two points on the left of the rectangle have an x-coordinate of 2, so the missing point must also have an x-coordinate of 2.
Therefore, the coordinates of the missing point are (2,9), which is choice D.