. 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. (1 point) B(); D()
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.
Given that A(3,2) and C(6,5) are diagonally opposite vertices of the rectangle, we can determine the length of the sides and find the coordinates of vertices B and D.
Length of side AD is the distance between points A and C:
AD = √((6 - 3)^2 + (5 - 2)^2)
AD = √(3^2 + 3^2)
AD = √(9 + 9)
AD = √18
AD = 3√2
Since opposite sides of the rectangle are equal, the length of side AB is also 3√2 units.
Now, we can determine the coordinates of vertex B.
From point A(3,2), we can move 3 units right and 2 units up to reach vertex B.
B(x, y) = (3 + 3, 2 + 3)
B(x, y) = (6, 5)
Therefore, the coordinates of vertex B are B(6,5).
Similarly, we can determine the coordinates of vertex D.
From point C(6,5), we can move 3 units left and 2 units down to reach vertex D.
D(x, y) = (6 - 3, 5 - 2)
D(x, y) = (3, 3)
Therefore, the coordinates of vertex D are D(3,3).
. Find the length of line segment BC . (1 point) Responses 3 cm 3 cm 9 cm 9 cm 8 cm 8 cm 10 cm
To find the length of line segment BC, we need to compute the distance between points B(6,5) and C(6,5).
BC = √((6 - 6)^2 + (5 - 5)^2)
BC = √(0^2 + 0^2)
BC = √0
BC = 0
Therefore, the length of line segment BC is 0 cm.
pick one i put
8 cm
. Point A and Point D have the same second coordinate, and ABCD is a quadrilateral. Line segment AD is 3 cm in length. What coordinates does Point D need to be plotted at to make this statement true? (1 point) Responses (6, −4) left parenthesis 6 comma negative 4 right parenthesis (−2, 4) left parenthesis negative 2 comma 4 right parenthesis (4, −6) left parenthesis 4 comma negative 6 right parenthesis (−6, 4) left parenthesis negative 6 comma 4 right parenthesis
Since point A and point D have the same second coordinate, D needs to have a y-coordinate that is the same as that of point A. Given that point A is at A(3,2), point D needs to have a y-coordinate of 2.
With a line segment AD of 3 cm in length, the x-coordinate of point D can be determined as follows:
AD = √((x2 - x1)^2 + (y2 - y1)^2)
3 = √((x - 3)^2 + (2 - 2)^2)
3 = √((x - 3)^2)
9 = (x - 3)^2
±3 = x - 3
Solving for x gives:
x - 3 = ±3
x = 3 ± 3
So, the possible x-coordinates for point D are x=6 and x=0.
Therefore, the coordinates for point D need to be plotted at D(6,2) or D(0,2). Among the options provided, (6,2) corresponds to Point D.
Correct Response: (6,2)
Find the perimeter of the polygon in kilometers. (1 point) Responses 46 square kilometers 46 square kilometers 104 square kilometers 104 square kilometers 34 square kilometers 34 square kilometers 46 kilometers
To find the perimeter of the polygon, we need to sum the lengths of all the sides.
Using the coordinate points provided:
A(3,2), B(6,5), C(6,5), D(3,2)
The lengths of the sides can be determined as follows:
AB = √((6 - 3)^2 + (5 - 2)^2)
AB = √(3^2 + 3^2)
AB = √(9 + 9)
AB = √18
BC = √((6 - 6)^2 + (5 - 5)^2)
BC = √0
BC = 0
CD = √((3 - 6)^2 + (2 - 5)^2)
CD = √(3^2 + 3^2)
CD = √(9 + 9)
CD = √18
DA = √((3 - 3)^2 + (2 - 2)^2)
DA = √0
DA = 0
Now, summing the lengths of all the sides:
Perimeter = AB + BC + CD + DA
Perimeter = √18 + 0 + √18 + 0
Perimeter = 2√18
Perimeter = 6√2
Therefore, the perimeter of the polygon is 6√2 kilometers. Among the provided options, 46 kilometers is closest to 6√2.
Correct Response: 46 kilometers