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Three vertices of a rectangle in the standard (x,y) coordinate plane have the coordinates (−2,3), (4,3) and (4,2). What are the coordinates of the fourth vertex?
- a)(−2, −2)
- b)(3, −3)
- c)(−3, 3)
- d)(2, −2)
- e)(−2, 2)
Correct answer is option 'E'. Can you explain this answer?
Most Upvoted Answer
Three vertices of a rectangle in the standard (x,y) coordinate plane h...
The correct answer is E. Graph the rectangle on a coordinate graph.
As you can see from the graph, the fourth vertex must be (−2, 2).
As you can see from the graph, the fourth vertex must be (−2, 2).
Community Answer
Three vertices of a rectangle in the standard (x,y) coordinate plane h...
Given Information:
Three vertices of a rectangle in the standard (x,y) coordinate plane are (−2,3), (4,3), and (4,2).
Explanation:
Finding the Fourth Vertex:
To find the coordinates of the fourth vertex of the rectangle, we need to understand the properties of a rectangle in a coordinate plane.
Property of a Rectangle:
In a rectangle, opposite sides are equal in length and parallel. So, if we consider the side with coordinates (−2,3) and (4,3), the other side parallel to it must be a vertical line passing through (4,2).
Calculating the Fourth Vertex:
Since the opposite sides of a rectangle are parallel, the y-coordinate of the fourth vertex will be the same as the y-coordinate of the point (4,2). Therefore, the y-coordinate of the fourth vertex is 2.
Now, as the opposite sides of the rectangle are equal, the x-coordinate of the fourth vertex will be the same as the x-coordinate of the point (−2,3). Therefore, the x-coordinate of the fourth vertex is −2.
Hence, the coordinates of the fourth vertex are (−2,2).
Therefore, the correct answer is option (E) (−2, 2).
Three vertices of a rectangle in the standard (x,y) coordinate plane are (−2,3), (4,3), and (4,2).
Explanation:
Finding the Fourth Vertex:
To find the coordinates of the fourth vertex of the rectangle, we need to understand the properties of a rectangle in a coordinate plane.
Property of a Rectangle:
In a rectangle, opposite sides are equal in length and parallel. So, if we consider the side with coordinates (−2,3) and (4,3), the other side parallel to it must be a vertical line passing through (4,2).
Calculating the Fourth Vertex:
Since the opposite sides of a rectangle are parallel, the y-coordinate of the fourth vertex will be the same as the y-coordinate of the point (4,2). Therefore, the y-coordinate of the fourth vertex is 2.
Now, as the opposite sides of the rectangle are equal, the x-coordinate of the fourth vertex will be the same as the x-coordinate of the point (−2,3). Therefore, the x-coordinate of the fourth vertex is −2.
Hence, the coordinates of the fourth vertex are (−2,2).
Therefore, the correct answer is option (E) (−2, 2).
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Three vertices of a rectangle in the standard (x,y) coordinate plane have the coordinates (−2,3), (4,3) and (4,2). What are the coordinates of the fourth vertex?a)(−2, −2)b)(3, −3)c)(−3, 3)d)(2, −2)e)(−2, 2)Correct answer is option 'E'. Can you explain this answer?
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Three vertices of a rectangle in the standard (x,y) coordinate plane have the coordinates (−2,3), (4,3) and (4,2). What are the coordinates of the fourth vertex?a)(−2, −2)b)(3, −3)c)(−3, 3)d)(2, −2)e)(−2, 2)Correct answer is option 'E'. Can you explain this answer? for ACT 2025 is part of ACT preparation. The Question and answers have been prepared according to the ACT exam syllabus. Information about Three vertices of a rectangle in the standard (x,y) coordinate plane have the coordinates (−2,3), (4,3) and (4,2). What are the coordinates of the fourth vertex?a)(−2, −2)b)(3, −3)c)(−3, 3)d)(2, −2)e)(−2, 2)Correct answer is option 'E'. Can you explain this answer? covers all topics & solutions for ACT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Three vertices of a rectangle in the standard (x,y) coordinate plane have the coordinates (−2,3), (4,3) and (4,2). What are the coordinates of the fourth vertex?a)(−2, −2)b)(3, −3)c)(−3, 3)d)(2, −2)e)(−2, 2)Correct answer is option 'E'. Can you explain this answer?.
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