Question

If the centroid of the triangle formed by the points
(3,5), (-7,4), (10,-k) is at the
formed by the points
point (K-1) then K= ?

plz answer with explanation​

Answer 1

answer is k equal to 3

X 1 + X 2 + x3 upon 3 and Y1 + Y2 + y 3 upon 3 this is the centroid formula

put the value inside X and Y that is 3 in x minus 5 Y - 7 in X 4 in y and 10 in X and minus k in y

and simply solve you will get the answer that is k

equal to 3

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Answer 2

The value of k is 2.

Given: the points ( 3 , - 5 ), ( - 7 , 4 ), ( 10 , -k )

The centroid of the triangle is ( k, - 1 )

To Find: The value of k.

Solution:

• There is a slight moderation in the question. The point ( 3, 5) must be (3, - 5 ) and the centroid of the triangle should be ( k, - 1 ).
• The centroid is the point at which the three medians of the triangle intersect and is known as the centroid of a triangle.
• The centroid of a triangle can be calculated using the formula,

        C ( a , b ) ≡ (( x1 + x2 + x3 )/3 ) , ( y1 + y2 + y3 )/3 )

where ( x1, y1 ), ( x2, y2 ), and ( x3, y3 ) are the vertices of a triangle.

Using the formula in our question, we get;

       C ( k , -1 ) ≡ (( 3 - 7 + 10 )/3 ) , ( - 5 + 4 - k )/3 )

                        ≡  ( 6 / 3 , ( -1 - k ) / 3 )

                        ≡ ( 2 , ( -1 - k ) / 3 )

So now, comparing both sides we get,

          k = 2  or  -1 - k  / 3 = -1

In both cases, we get k = 2.

Hence, the value of k is 2.

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