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If p(1,2),q(4,6),r(5,7),s(a,b)are the vertices of parallelogram pqrs then find the values of a and b?
Most Upvoted Answer
If p(1,2),q(4,6),r(5,7),s(a,b)are the vertices of parallelogram pqrs t...
Solution:
Given, the vertices of the parallelogram PQRS are:
P(1,2), Q(4,6), R(5,7) and S(a,b)
Let us first find the coordinates of the fourth vertex S.
Using the property of the parallelogram, we know that the opposite sides of the parallelogram are parallel and equal in length.
Therefore, we can find the coordinates of S as follows:
Coordinate of S = Coordinate of Q + Coordinate of R - Coordinate of P
Using the above formula, we get:
S(a,b) = Q(4,6) + R(5,7) - P(1,2)
S(a,b) = (4+5-1, 6+7-2)
S(a,b) = (8,11)
Therefore, the coordinates of the fourth vertex S are (8,11).
Now, we can find the value of a and b by equating the coordinates of S.
Equating the x and y coordinates, we get:
a = 8
b = 11
Hence, the values of a and b are 8 and 11 respectively.
Final Answer:
The values of a and b are 8 and 11 respectively.
Given, the vertices of the parallelogram PQRS are:
P(1,2), Q(4,6), R(5,7) and S(a,b)
Let us first find the coordinates of the fourth vertex S.
Using the property of the parallelogram, we know that the opposite sides of the parallelogram are parallel and equal in length.
Therefore, we can find the coordinates of S as follows:
Coordinate of S = Coordinate of Q + Coordinate of R - Coordinate of P
Using the above formula, we get:
S(a,b) = Q(4,6) + R(5,7) - P(1,2)
S(a,b) = (4+5-1, 6+7-2)
S(a,b) = (8,11)
Therefore, the coordinates of the fourth vertex S are (8,11).
Now, we can find the value of a and b by equating the coordinates of S.
Equating the x and y coordinates, we get:
a = 8
b = 11
Hence, the values of a and b are 8 and 11 respectively.
Final Answer:
The values of a and b are 8 and 11 respectively.
Community Answer
If p(1,2),q(4,6),r(5,7),s(a,b)are the vertices of parallelogram pqrs t...
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If p(1,2),q(4,6),r(5,7),s(a,b)are the vertices of parallelogram pqrs then find the values of a and b?
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If p(1,2),q(4,6),r(5,7),s(a,b)are the vertices of parallelogram pqrs then find the values of a and b? 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 If p(1,2),q(4,6),r(5,7),s(a,b)are the vertices of parallelogram pqrs then find the values of a and b? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If p(1,2),q(4,6),r(5,7),s(a,b)are the vertices of parallelogram pqrs then find the values of a and b?.
If p(1,2),q(4,6),r(5,7),s(a,b)are the vertices of parallelogram pqrs then find the values of a and b? 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 If p(1,2),q(4,6),r(5,7),s(a,b)are the vertices of parallelogram pqrs then find the values of a and b? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If p(1,2),q(4,6),r(5,7),s(a,b)are the vertices of parallelogram pqrs then find the values of a and b?.
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