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Two vertices of a triangle are (2, -4) and (1, 3). If the origin is the centroid of the triangle then what is the third vertex?
- a)(1, 3)
- b)(-3, 1)
- c)(1, -1)
- d)(3, -3)
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
Two vertices of a triangle are (2, -4) and (1, 3). If the origin is th...
Explanation:
- Given vertices of the triangle: A(2, -4) and B(1, 3)
- Let C(x, y) be the third vertex of the triangle
Centroid of a Triangle:
- The centroid of a triangle is the point of intersection of the medians of the triangle.
- The centroid divides each median into two segments, with the segment closer to the vertex being twice as long as the segment closer to the midpoint of the opposite side.
Coordinates of the Centroid:
- The coordinates of the centroid of a triangle with vertices A(x1, y1), B(x2, y2), and C(x3, y3) are ((x1 + x2 + x3)/3, (y1 + y2 + y3)/3)
Finding the Third Vertex:
- Given that the origin (0, 0) is the centroid of the triangle
- Using the centroid formula, we have (2 + 1 + x)/3 = 0 and (-4 + 3 + y)/3 = 0
- Solving these equations, we get x = -3 and y = 1
- Therefore, the third vertex is C(-3, 1)
Conclusion:
- The third vertex of the triangle is (-3, 1) which corresponds to option B.
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Two vertices of a triangle are (2, -4) and (1, 3). If the origin is th...
third vertex = (-3, 1)
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Two vertices of a triangle are (2, -4) and (1, 3). If the origin is the centroid of the triangle then what is the third vertex?a)(1, 3)b)(-3, 1)c)(1, -1)d)(3, -3)Correct answer is option 'B'. Can you explain this answer?
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