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The three points A (3, 0, 3), B (5, 3, 2), C (6, 5, 5) form ________.
- a)equilateral triangle
- b)right angled triangle
- c)isosceles triangle
- d)right angled isosceles triangle
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
The three points A (3, 0, 3), B (5, 3, 2), C (6, 5, 5) form ________.a...
Explanation:
To determine whether the given points A, B, and C form an isosceles triangle, we need to examine the lengths of the three sides of the triangle.
Calculating the lengths of the sides:
We can use the distance formula to calculate the lengths of the sides of the triangle. The distance formula is given by:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2)
Applying the distance formula to the given points:
- The distance between points A and B:
dAB = sqrt((5 - 3)^2 + (3 - 0)^2 + (2 - 3)^2) = sqrt(4 + 9 + 1) = sqrt(14)
- The distance between points B and C:
dBC = sqrt((6 - 5)^2 + (5 - 3)^2 + (5 - 2)^2) = sqrt(1 + 4 + 9) = sqrt(14)
- The distance between points C and A:
dCA = sqrt((3 - 6)^2 + (0 - 5)^2 + (3 - 5)^2) = sqrt(9 + 25 + 4) = sqrt(38)
Comparing the lengths of the sides:
We can see that dAB = dBC = sqrt(14). However, dCA = sqrt(38), which is not equal to dAB or dBC.
Since at least two sides of the triangle are not equal in length, the triangle formed by points A, B, and C is not an equilateral triangle.
Conclusion:
The three points A (3, 0, 3), B (5, 3, 2), and C (6, 5, 5) form an isosceles triangle.
To determine whether the given points A, B, and C form an isosceles triangle, we need to examine the lengths of the three sides of the triangle.
Calculating the lengths of the sides:
We can use the distance formula to calculate the lengths of the sides of the triangle. The distance formula is given by:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2)
Applying the distance formula to the given points:
- The distance between points A and B:
dAB = sqrt((5 - 3)^2 + (3 - 0)^2 + (2 - 3)^2) = sqrt(4 + 9 + 1) = sqrt(14)
- The distance between points B and C:
dBC = sqrt((6 - 5)^2 + (5 - 3)^2 + (5 - 2)^2) = sqrt(1 + 4 + 9) = sqrt(14)
- The distance between points C and A:
dCA = sqrt((3 - 6)^2 + (0 - 5)^2 + (3 - 5)^2) = sqrt(9 + 25 + 4) = sqrt(38)
Comparing the lengths of the sides:
We can see that dAB = dBC = sqrt(14). However, dCA = sqrt(38), which is not equal to dAB or dBC.
Since at least two sides of the triangle are not equal in length, the triangle formed by points A, B, and C is not an equilateral triangle.
Conclusion:
The three points A (3, 0, 3), B (5, 3, 2), and C (6, 5, 5) form an isosceles triangle.
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Community Answer
The three points A (3, 0, 3), B (5, 3, 2), C (6, 5, 5) form ________.a...
We know, distance between two points (x1, y1, z1) and (x2, y2, z2) is 
Since AB = BC so, it forms isosceles triangle.
Since AB = BC so, it forms isosceles triangle.
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The three points A (3, 0, 3), B (5, 3, 2), C (6, 5, 5) form ________.a)equilateral triangleb)right angled trianglec)isosceles triangled)right angled isosceles triangleCorrect answer is option 'C'. Can you explain this answer?
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