Use Coordinate Geometry to Solve Problems Quick Check
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Question
Use the image to answer the question.
An illustration shows quadrant one of a coordinate plane with the x axis extending from 0 to 9 and the y axis extending from 0 to 9 in increments of 1. A quadrilateral upper A upper B upper C upper D is drawn on the coordinate plane. The coordinates of the rectangle are as follows: upper A left parenthesis 2 comma 5 right parenthesis, upper B left parenthesis 1 comma 3 right parenthesis, upper C left parenthesis 9 comma 3 right parenthesis, and upper D left parenthesis 9 comma 6 right parenthesis.
Find the length of line segment BC.
(1 point)
Responses
9 cm
9 cm
10 cm
10 cm
3 cm
3 cm
8 cm
Here are the answers to the Coordinate Geometry Quick Check
1. 8cm
2. (-6,4)
3. 12 miles
4. 46 kilometers
5. 32 square feet
I just took the quick check and these are the correct answers.
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Use Coordinate Geometry to Solve Problems Quick Check
1 of 51 of 5 Items
Question
Use the image to answer the question.
An illustration shows quadrant one of a coordinate plane with the x axis extending from 0 to 9 and the y axis extending from 0 to 9 in increments of 1. A quadrilateral upper A upper B upper C upper D is drawn on the coordinate plane. The coordinates of the rectangle are as follows: upper A left parenthesis 2 comma 5 right parenthesis, upper B left parenthesis 1 comma 3 right parenthesis, upper C left parenthesis 9 comma 3 right parenthesis, and upper D left parenthesis 9 comma 6 right parenthesis.
Find the length of line segment BC.
(1 point)
Responses
9 cm
9 cm
10 cm
10 cm
3 cm
3 cm
8 cm
We can find the length of line segment BC by finding the distance between the coordinates of points B and C.
Using the Distance Formula, d = sqrt((x2 - x1)^2 + (y2 - y1)^2), we have:
d = sqrt((9 - 1)^2 + (3 - 3)^2)
d = sqrt(64)
d = 8
Therefore, the length of line segment BC is 8 units.
Answer: 8 cm
Use Coordinate Geometry to Solve Problems Quick Check
2 of 52 of 5 Items
Question
Use the image to answer the question.
An illustration shows a coordinate plane with the x axis extending from negative 11 to 2 and the y axis extending from negative 3 to 10 in increments of 1. Points upper A,upper B, and upper C are plotted in quadrant 2. Upper A is plotted at left parenthesis negative 9 comma 4 right parenthesis. Upper B is plotted at left parenthesis negative 11 comma 1 right parenthesis. Upper C is plotted at left parenthesis negative 2 comma 1 right parenthesis.
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)
(−6, 4)
(−2, 4)
(4, −6)
Since points A and D have the same second coordinate, D should be plotted at either (x, 4) or (-x, 4), where x is a positive number.
We can use the Distance Formula again to find the possible x-coordinates of point D that would make line segment AD equal to 3 units.
Let's assume that D is at (x, 4). Then, we have:
d = sqrt((x - (-9))^2 + (4 - 4)^2) = 3
sqrt((x+9)^2) = 3
x+9 = 3 or x+9 = -3
x = -6 or x = -12
Since x should be positive, the value of x that satisfies this condition is x = 6. Therefore, point D can be plotted at (6, 4) or at its reflection across the y-axis, which is (-6, 4).
Answer: (6, -4) or (-6, 4)
Apply the techniques of using the coordinates to find the length and the width of the polygon. Use the length and the width to find the perimeter of the polygon in miles. Rectangle ABCD has vertices point A (1,−3), point B (5, −3), point C (5, −1), and point D (1, −1).(1 point)
Responses
−12 miles
12 miles
12 square miles
8 square miles
We can use the Distance Formula to find the length and width of the rectangle:
Length AB = sqrt((5-1)^2 + (-3+3)^2) = 4 units
Width BC = sqrt((5-5)^2 + (-1+3)^2) = 2 units
Therefore, the perimeter of the rectangle is:
Perimeter = 2(Length + Width) = 2(4 + 2) = 12 units
Since the problem does not provide a unit of measurement, we cannot determine the answer in miles. However, the answer to the problem is 12 square units.
Answer: 12 square miles (or square units)
To find the length of line segment BC, you can use the distance formula in coordinate geometry. The distance formula is derived from the Pythagorean theorem and is used to find the distance between two points (x1, y1) and (x2, y2) in a coordinate plane.
The distance formula is given by:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
In this case, the coordinates of point B are (1, 3) and the coordinates of point C are (9, 3). Therefore, you can substitute these values into the distance formula:
d = sqrt((9 - 1)^2 + (3 - 3)^2)
Simplifying further:
d = sqrt(8^2 + 0^2)
d = sqrt(64)
d = 8
So the length of line segment BC is 8 units. Therefore, the correct answer is 8 cm.