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If the points A(6,1) B(8,2) C(9,4) and D(p,3) are the vertices of a parallelogram,taken in order, find the value of p?
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If the points A(6,1) B(8,2) C(9,4) and D(p,3) are the vertices of a pa...
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If the points A(6,1) B(8,2) C(9,4) and D(p,3) are the vertices of a pa...
Given:
Points A(6,1), B(8,2), C(9,4), and D(p,3) are the vertices of a parallelogram.
To find:
The value of p.
Solution:
A parallelogram is a quadrilateral with opposite sides parallel and equal in length. To determine the value of p, we can use the properties of a parallelogram.
Step 1: Find the slope of AB and CD.
The slope of a line passing through two points (x1, y1) and (x2, y2) is given by (y2 - y1) / (x2 - x1).
Slope of AB = (2 - 1) / (8 - 6) = 1/2
Slope of CD = (4 - 3) / (9 - p) = 1 / (9 - p)
Step 2: Since opposite sides of a parallelogram are parallel, the slopes of AB and CD should be equal.
Therefore, 1/2 = 1 / (9 - p)
Step 3: Cross multiply and solve for p.
1(9 - p) = 2(1)
9 - p = 2
-p = 2 - 9
-p = -7
p = 7
Answer:
The value of p is 7.
Points A(6,1), B(8,2), C(9,4), and D(p,3) are the vertices of a parallelogram.
To find:
The value of p.
Solution:
A parallelogram is a quadrilateral with opposite sides parallel and equal in length. To determine the value of p, we can use the properties of a parallelogram.
Step 1: Find the slope of AB and CD.
The slope of a line passing through two points (x1, y1) and (x2, y2) is given by (y2 - y1) / (x2 - x1).
Slope of AB = (2 - 1) / (8 - 6) = 1/2
Slope of CD = (4 - 3) / (9 - p) = 1 / (9 - p)
Step 2: Since opposite sides of a parallelogram are parallel, the slopes of AB and CD should be equal.
Therefore, 1/2 = 1 / (9 - p)
Step 3: Cross multiply and solve for p.
1(9 - p) = 2(1)
9 - p = 2
-p = 2 - 9
-p = -7
p = 7
Answer:
The value of p is 7.
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If the points A(6,1) B(8,2) C(9,4) and D(p,3) are the vertices of a parallelogram,taken in order, find the value of p?
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If the points A(6,1) B(8,2) C(9,4) and D(p,3) are the vertices of a parallelogram,taken in order, find the value of p? 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 the points A(6,1) B(8,2) C(9,4) and D(p,3) are the vertices of a parallelogram,taken in order, find the value of p? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the points A(6,1) B(8,2) C(9,4) and D(p,3) are the vertices of a parallelogram,taken in order, find the value of p?.
If the points A(6,1) B(8,2) C(9,4) and D(p,3) are the vertices of a parallelogram,taken in order, find the value of p? 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 the points A(6,1) B(8,2) C(9,4) and D(p,3) are the vertices of a parallelogram,taken in order, find the value of p? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the points A(6,1) B(8,2) C(9,4) and D(p,3) are the vertices of a parallelogram,taken in order, find the value of p?.
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