The centroid of the triangle, whose vertices are (3, -5), (-7, 4), (10,-2), is given bya)(6,-3)b)(2,-1)c)(3,-3/2)d)none of the aboveCorrect answer is option 'B'. Can you explain this answer?

Question

Answer

The coordinates of the centroid will be

Answer

The centroid of a triangle can be found by taking the average of the coordinates of its vertices.

The given triangle has vertices at (3, -5), (-7, 4), and (10, -2). To find the centroid, we need to find the average of the x-coordinates and the average of the y-coordinates.

Finding the x-coordinate of the centroid:
The x-coordinate of the centroid is given by the formula:
x = (x1 + x2 + x3) / 3

Using the coordinates of the vertices, we have:
x = (3 + (-7) + 10) / 3
x = 6 / 3
x = 2

Therefore, the x-coordinate of the centroid is 2.

Finding the y-coordinate of the centroid:
The y-coordinate of the centroid is given by the formula:
y = (y1 + y2 + y3) / 3

Using the coordinates of the vertices, we have:
y = (-5 + 4 + (-2)) / 3
y = -3 / 3
y = -1

Therefore, the y-coordinate of the centroid is -1.

Hence, the centroid of the triangle is (2, -1), which corresponds to option B.

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