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Three consecutive vertices of a parallelogram are (1, –2), (3, 6) and (5, 10). The coordinates of the fourth vertex are :
- a)(–3, 2)
- b)(2, – 3)
- c)(3, 2)
- d)(–2, –3)
Correct answer is option 'C'. Can you explain this answer?
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Three consecutive vertices of a parallelogram are (1, –2), (3, 6...
Let's call the three consecutive vertices of the parallelogram (1, y1), (x2, y2), and (x3, y3). Since opposite sides of a parallelogram are parallel, the slope of the line passing through (1, y1) and (x2, y2) is equal to the slope of the line passing through (x3, y3) and (x2, y2).
The slope of a line passing through two points (x1, y1) and (x2, y2) is given by (y2 - y1) / (x2 - x1).
Therefore, the slope of the line passing through (1, y1) and (x2, y2) is (y2 - y1) / (x2 - 1).
Similarly, the slope of the line passing through (x3, y3) and (x2, y2) is (y2 - y3) / (x2 - x3).
Since these slopes are equal, we have:
(y2 - y1) / (x2 - 1) = (y2 - y3) / (x2 - x3)
Cross multiplying gives:
(x2 - x3)(y2 - y1) = (x2 - 1)(y2 - y3)
Expanding both sides gives:
x2y2 - x2y1 - x3y2 + x3y1 = x2y2 - x2y3 - y2 + y3
Rearranging terms gives:
x3y2 - x3y1 - y2 + y3 = -x2y1 + x2y3
Factoring out x3 and x2 gives:
x3(y2 - y1) - (y2 - y3) = -x2(y1 - y3)
Now we can see that the left side of the equation is equal to the right side of the equation.
Therefore, the equation is satisfied for any values of x2, y2, x3, and y3, as long as they satisfy the equation x3(y2 - y1) - (y2 - y3) = -x2(y1 - y3).
The slope of a line passing through two points (x1, y1) and (x2, y2) is given by (y2 - y1) / (x2 - x1).
Therefore, the slope of the line passing through (1, y1) and (x2, y2) is (y2 - y1) / (x2 - 1).
Similarly, the slope of the line passing through (x3, y3) and (x2, y2) is (y2 - y3) / (x2 - x3).
Since these slopes are equal, we have:
(y2 - y1) / (x2 - 1) = (y2 - y3) / (x2 - x3)
Cross multiplying gives:
(x2 - x3)(y2 - y1) = (x2 - 1)(y2 - y3)
Expanding both sides gives:
x2y2 - x2y1 - x3y2 + x3y1 = x2y2 - x2y3 - y2 + y3
Rearranging terms gives:
x3y2 - x3y1 - y2 + y3 = -x2y1 + x2y3
Factoring out x3 and x2 gives:
x3(y2 - y1) - (y2 - y3) = -x2(y1 - y3)
Now we can see that the left side of the equation is equal to the right side of the equation.
Therefore, the equation is satisfied for any values of x2, y2, x3, and y3, as long as they satisfy the equation x3(y2 - y1) - (y2 - y3) = -x2(y1 - y3).
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Three consecutive vertices of a parallelogram are (1, –2), (3, 6) and (5, 10). The coordinates of the fourth vertexare :a)(–3, 2)b)(2, – 3)c)(3, 2)d)(–2, –3)Correct answer is option 'C'. Can you explain this answer?
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Three consecutive vertices of a parallelogram are (1, –2), (3, 6) and (5, 10). The coordinates of the fourth vertexare :a)(–3, 2)b)(2, – 3)c)(3, 2)d)(–2, –3)Correct answer is option 'C'. Can you explain this answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Three consecutive vertices of a parallelogram are (1, –2), (3, 6) and (5, 10). The coordinates of the fourth vertexare :a)(–3, 2)b)(2, – 3)c)(3, 2)d)(–2, –3)Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Three consecutive vertices of a parallelogram are (1, –2), (3, 6) and (5, 10). The coordinates of the fourth vertexare :a)(–3, 2)b)(2, – 3)c)(3, 2)d)(–2, –3)Correct answer is option 'C'. Can you explain this answer?.
Three consecutive vertices of a parallelogram are (1, –2), (3, 6) and (5, 10). The coordinates of the fourth vertexare :a)(–3, 2)b)(2, – 3)c)(3, 2)d)(–2, –3)Correct answer is option 'C'. Can you explain this answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Three consecutive vertices of a parallelogram are (1, –2), (3, 6) and (5, 10). The coordinates of the fourth vertexare :a)(–3, 2)b)(2, – 3)c)(3, 2)d)(–2, –3)Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Three consecutive vertices of a parallelogram are (1, –2), (3, 6) and (5, 10). The coordinates of the fourth vertexare :a)(–3, 2)b)(2, – 3)c)(3, 2)d)(–2, –3)Correct answer is option 'C'. Can you explain this answer?.
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Three consecutive vertices of a parallelogram are (1, –2), (3, 6) and (5, 10). The coordinates of the fourth vertexare :a)(–3, 2)b)(2, – 3)c)(3, 2)d)(–2, –3)Correct answer is option 'C'. Can you explain this answer?, a detailed solution for Three consecutive vertices of a parallelogram are (1, –2), (3, 6) and (5, 10). The coordinates of the fourth vertexare :a)(–3, 2)b)(2, – 3)c)(3, 2)d)(–2, –3)Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of Three consecutive vertices of a parallelogram are (1, –2), (3, 6) and (5, 10). The coordinates of the fourth vertexare :a)(–3, 2)b)(2, – 3)c)(3, 2)d)(–2, –3)Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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