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A triangle is formed by the following points:
A = (1,2), B = (4,2), C = (4,6)
What are the co-ordinated of the centre of circle that circumscribes triangle ABC..
A = (1,2), B = (4,2), C = (4,6)
What are the co-ordinated of the centre of circle that circumscribes triangle ABC..
- a)(4.5,3.5)
- b)(2.5,4)
- c)(3,2.5)
- d)(0,0)
- e)(0.5,5)
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
A triangle is formed by the following points:A = (1,2), B = (4,2), C =...
To find the coordinates of the center of the circle that circumscribes triangle ABC, we can use the properties of the circumcenter.
The circumcenter is the intersection point of the perpendicular bisectors of the sides of the triangle. These perpendicular bisectors are the lines that pass through the midpoints of each side and are perpendicular to those sides.
Let's calculate the midpoints of the sides AB, BC, and AC:
Midpoint of AB = ((1+4)/2, (2+2)/2) = (2.5, 2) Midpoint of BC = ((4+4)/2, (2+6)/2) = (4, 4) Midpoint of AC = ((1+4)/2, (2+6)/2) = (2.5, 4)
Next, we need to find the equations of the perpendicular bisectors of AB and BC.
The slope of AB is (2-2)/(4-1) = 0/3 = 0. The negative reciprocal of 0 is undefined. Therefore, the equation of the perpendicular bisector of AB is a vertical line passing through the midpoint (2.5, 2), which can be written as x = 2.5.
The slope of BC is (6-2)/(4-4) = 4/0, which is undefined. Therefore, the equation of the perpendicular bisector of BC is a horizontal line passing through the midpoint (4, 4), which can be written as y = 4.
The point of intersection of these two lines, x = 2.5 and y = 4, gives us the coordinates of the circumcenter.
Hence, the coordinates of the center of the circle that circumscribes triangle ABC are (2.5, 4).
Therefore, the correct answer is B: (2.5, 4).
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A triangle is formed by the following points:A = (1,2), B = (4,2), C = (4,6)What are the co-ordinated of the centre of circle that circumscribes triangle ABC..a)(4.5,3.5)b)(2.5,4)c)(3,2.5)d)(0,0)e)(0.5,5)Correct answer is option 'B'. Can you explain this answer?
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