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For the triangle whose sides are along the lines x = 0, y = 0 and x/6+y/8 = 1, the incentre is :
- a)(3, 4)
- b)(2, 2)
- c)(2, 3)
- d)(3, 2)
Correct answer is option 'C'. Can you explain this answer?
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For the triangle whose sides are along the lines x = 0, y = 0 and x/6+...
Finding the Incentre of a Triangle
To find the incentre of a triangle, we need to find the point where the angle bisectors of the triangle meet. The angle bisectors are the lines that divide the angles of the triangle into two equal parts. The incentre is the intersection of these angle bisectors and is equidistant from all three sides of the triangle.
Given Triangle
The triangle in the question has sides along the lines x = 0, y = 0 and x/6 y/8 = 1. Let's first plot these lines on a graph to get a visual representation of the triangle.
We can see that the triangle is a right-angled triangle with vertices at (0, 0), (6, 0) and (0, 8). Now, let's find the equation of the angle bisectors of this triangle.
Finding the Equation of Angle Bisectors
To find the equation of the angle bisectors, we need to first find the equations of the two lines that form each angle. We can then find the midpoint of these lines and the slope of the angle bisector. Finally, we can use the point-slope form of a line to find the equation of the angle bisector.
Let's start with the angle formed by sides (0, 0) to (6, 0) and (0, 8). The equation of the line joining these two points is y = -3/4x + 8. Now, let's find the equation of the line perpendicular to this line that passes through the midpoint of the line segment joining (0, 0) and (6, 0).
The midpoint of the line segment joining (0, 0) and (6, 0) is (3, 0). The slope of the line joining (0, 0) and (6, 0) is 0. Therefore, the slope of the line perpendicular to this line is undefined (since it is a vertical line). The equation of the line passing through (3, 0) with undefined slope is x = 3.
Using the same method, we can find the equation of the angle bisector of the angle formed by sides (0, 0) to (0, 8) and (6, 0). The equation of the line joining these two points is y = 8/6x = 4/3x. The midpoint of the line segment joining (0, 0) and (0, 8) is (0, 4). The slope of the line joining (0, 0) and (0, 8) is undefined. Therefore, the slope of the line perpendicular to this line is 0. The equation of the line passing through (0, 4) with slope 0 is y = 4.
Intersection of Angle Bisectors
Now that we have the equations of the two angle bisectors, we can find their intersection point, which is the incentre of the triangle. The intersection point is the solution to the system of equations:
x = 3
y = 4
y = 4
The solution to this system of equations is (3, 4), which is option (c). Therefore, the incentre of the triangle whose sides are along the lines x = 0, y = 0 and x/6 y/8 = 1 is
To find the incentre of a triangle, we need to find the point where the angle bisectors of the triangle meet. The angle bisectors are the lines that divide the angles of the triangle into two equal parts. The incentre is the intersection of these angle bisectors and is equidistant from all three sides of the triangle.
Given Triangle
The triangle in the question has sides along the lines x = 0, y = 0 and x/6 y/8 = 1. Let's first plot these lines on a graph to get a visual representation of the triangle.
We can see that the triangle is a right-angled triangle with vertices at (0, 0), (6, 0) and (0, 8). Now, let's find the equation of the angle bisectors of this triangle.
Finding the Equation of Angle Bisectors
To find the equation of the angle bisectors, we need to first find the equations of the two lines that form each angle. We can then find the midpoint of these lines and the slope of the angle bisector. Finally, we can use the point-slope form of a line to find the equation of the angle bisector.
Let's start with the angle formed by sides (0, 0) to (6, 0) and (0, 8). The equation of the line joining these two points is y = -3/4x + 8. Now, let's find the equation of the line perpendicular to this line that passes through the midpoint of the line segment joining (0, 0) and (6, 0).
The midpoint of the line segment joining (0, 0) and (6, 0) is (3, 0). The slope of the line joining (0, 0) and (6, 0) is 0. Therefore, the slope of the line perpendicular to this line is undefined (since it is a vertical line). The equation of the line passing through (3, 0) with undefined slope is x = 3.
Using the same method, we can find the equation of the angle bisector of the angle formed by sides (0, 0) to (0, 8) and (6, 0). The equation of the line joining these two points is y = 8/6x = 4/3x. The midpoint of the line segment joining (0, 0) and (0, 8) is (0, 4). The slope of the line joining (0, 0) and (0, 8) is undefined. Therefore, the slope of the line perpendicular to this line is 0. The equation of the line passing through (0, 4) with slope 0 is y = 4.
Intersection of Angle Bisectors
Now that we have the equations of the two angle bisectors, we can find their intersection point, which is the incentre of the triangle. The intersection point is the solution to the system of equations:
x = 3
y = 4
y = 4
The solution to this system of equations is (3, 4), which is option (c). Therefore, the incentre of the triangle whose sides are along the lines x = 0, y = 0 and x/6 y/8 = 1 is
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For the triangle whose sides are along the lines x = 0, y = 0 and x/6+...
Sorry m unable to explain the option...yeah but its option C...
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For the triangle whose sides are along the lines x = 0, y = 0 and x/6+y/8 = 1,the incentre is :a)(3, 4)b)(2, 2)c)(2, 3)d)(3, 2)Correct answer is option 'C'. Can you explain this answer?
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