Rectangle ABCD has vertices A(3,2) and C(6,5) . What are the coordinates for vertices B and D ? Use the graph to help you determine the correct answers. Note, the vertex labels are located counterclockwise on the graph.
To find the coordinates for vertices B and D, we can use the fact that a rectangle has opposite sides that are equal in length and parallel to each other.
First, we can calculate the length of side AB by finding the distance between points A(3,2) and C(6,5) using the distance formula:
AB = √[(6-3)^2 + (5-2)^2]
AB = √(3^2 + 3^2)
AB = √(9 + 9) = √18
Since AB is equal in length to side CD, which is a horizontal line passing through point C(6,5), we can determine the coordinates of point D by moving 3 units to the left of point C along the x-axis:
D(x, y) = (6-3, 5) = (3,5)
Similarly, since BC is equal in length to side AD, which is a vertical line passing through point A(3,2), we can determine the coordinates of point B by moving 3 units up from point A along the y-axis:
B(x, y) = (3, 2+3) = (3,5)
Therefore, the coordinates for vertices B and D are:
B(3,5)
D(3,5)
b is not right
Apologies for the error in my previous response. Let's find the correct coordinates for vertices B and D.
Given that rectangle ABCD has vertices A(3,2) and C(6,5), we can determine the coordinates for vertices B and D as follows:
1. To find the coordinate for vertex D:
D is located directly opposite vertex A, so we can use the same x-coordinate as A(3) and the same y-coordinate as C(5).
Therefore, D is located at D(3, 5).
2. To find the coordinate for vertex B:
B is located directly opposite vertex C, so we can use the same x-coordinate as C(6) and the same y-coordinate as A(2).
Therefore, B is located at B(6, 2).
Therefore, the correct coordinates for vertices B and D are:
B(6, 2)
D(3, 5)