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Determine algebraically the vertices of Triangle formed by the lines 2 x minus y is equals to 2 x minus 3 Y is equals to 9 and y-axis?
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Determine algebraically the vertices of Triangle formed by the lines 2...
The given equations of the sides of triangle are,
2x - y = 9 , 2x - 3y = 9 , x = 0 (y-axis)
The vertices are obtained by solving the equations two at a time
Solving equations (1) and (2):
2x - y = 2x - 3y = 9
=> 2y = 0 (or) y = 0
=> x = 9/2
Solving (1) and (3):
2x - y = 9 and x = 0
=> y = -9
Solving (2) and (3):
2x - 3y = 9 and x = 0
=> y =9/-3 = -3
Therefore the vertices are A(9/2,0), B(0,-9) and C(0,-3)
2x - y = 9 , 2x - 3y = 9 , x = 0 (y-axis)
The vertices are obtained by solving the equations two at a time
Solving equations (1) and (2):
2x - y = 2x - 3y = 9
=> 2y = 0 (or) y = 0
=> x = 9/2
Solving (1) and (3):
2x - y = 9 and x = 0
=> y = -9
Solving (2) and (3):
2x - 3y = 9 and x = 0
=> y =9/-3 = -3
Therefore the vertices are A(9/2,0), B(0,-9) and C(0,-3)
Community Answer
Determine algebraically the vertices of Triangle formed by the lines 2...
Problem: Determine algebraically the vertices of Triangle formed by the lines 2 x minus y is equals to 2 x minus 3 Y is equals to 9 and y-axis?
Solution:
Step 1: Find the intersection points of the given lines.
We have two equations:
2 x - y = 9 ...(1)
2 x - 3 y = 9 ...(2)
To find the intersection of these two lines, we need to solve these equations simultaneously.
Subtracting Equation (1) from Equation (2), we get:
-2y = 0
y = 0
Substituting y = 0 in Equation (1), we get:
2x - 0 = 9
x = 4.5
So, the first intersection point is (4.5, 0).
Substituting y = 0 in Equation (2), we get:
2x - 3(0) = 9
x = 4.5
So, the second intersection point is also (4.5, 0).
Step 2: Find the third vertex of the triangle.
The third vertex lies on the y-axis. Therefore, its x-coordinate is zero.
Substituting x = 0 in Equation (1), we get:
2(0) - y = 9
y = -9
So, the third vertex is (0, -9).
Step 3: Plot the vertices and draw the triangle.
The three vertices of the triangle are:
(4.5, 0), (4.5, 0), and (0, -9)
Plotting these points on the graph and drawing a line to connect them, we get the triangle.
The vertices of the triangle are:
(4.5, 0), (4.5, 0), and (0, -9)
Note: The two vertices (4.5, 0) are the same point, so the triangle is actually a straight line.
Solution:
Step 1: Find the intersection points of the given lines.
We have two equations:
2 x - y = 9 ...(1)
2 x - 3 y = 9 ...(2)
To find the intersection of these two lines, we need to solve these equations simultaneously.
Subtracting Equation (1) from Equation (2), we get:
-2y = 0
y = 0
Substituting y = 0 in Equation (1), we get:
2x - 0 = 9
x = 4.5
So, the first intersection point is (4.5, 0).
Substituting y = 0 in Equation (2), we get:
2x - 3(0) = 9
x = 4.5
So, the second intersection point is also (4.5, 0).
Step 2: Find the third vertex of the triangle.
The third vertex lies on the y-axis. Therefore, its x-coordinate is zero.
Substituting x = 0 in Equation (1), we get:
2(0) - y = 9
y = -9
So, the third vertex is (0, -9).
Step 3: Plot the vertices and draw the triangle.
The three vertices of the triangle are:
(4.5, 0), (4.5, 0), and (0, -9)
Plotting these points on the graph and drawing a line to connect them, we get the triangle.
The vertices of the triangle are:
(4.5, 0), (4.5, 0), and (0, -9)
Note: The two vertices (4.5, 0) are the same point, so the triangle is actually a straight line.
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Determine algebraically the vertices of Triangle formed by the lines 2 x minus y is equals to 2 x minus 3 Y is equals to 9 and y-axis?
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Determine algebraically the vertices of Triangle formed by the lines 2 x minus y is equals to 2 x minus 3 Y is equals to 9 and y-axis? 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 Determine algebraically the vertices of Triangle formed by the lines 2 x minus y is equals to 2 x minus 3 Y is equals to 9 and y-axis? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Determine algebraically the vertices of Triangle formed by the lines 2 x minus y is equals to 2 x minus 3 Y is equals to 9 and y-axis?.
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