Question

if the centroid of the triangle formed by (x,0), (5,-2) and (-8,y) is at (-2,1) then (x,y) is equal to​

Answer 1

Step-by-step explanation:

Given :-

The centroid of the triangle formed by (x,0), (5,-2) and (-8,y) is at (-2,1)

To find :-

Find the point (x,y) ?

Solution :-

Given points are (x,0), (5,-2) and (-8,y)

Let (x1, y1) = (x,0) => x1 = x and y1 = 0

Let (x2, y2) = (5,-2) => x2 = 5 and y2 = -2

Let (x3, y3) = (-8,y) => x3 = -8 and y3 = y

We know that

The coordinates of the centroid of a triangle formed the three vertices is

G = ( (x1+x2+x3)/3 , (y1+y2+y3)/3 )

On substituting these values in the above formula then

=> G = ((x+5-8)/3 , (0-2+y)/3 )

=> G = ( (x-3)/3 , (y-2)/3 )

According to the given problem

The centroid = (-2,1)

=> ( (x-3)/3 , (y-2)/3 ) = (-2,1)

On comparing both sides then

=> (x-3)/3 = -2 and (y-2)/3 = 1

=> x-3 = -2×3 and y-2 = 1×3

=> x-3 = -6 and y-2 = 3

=> x = -6+3 and y = 3+2

=> x = -3 and y = 5

Therefore, (x,y) = (-3,5)

Answer:-

The point (x,y) = (-3,5) for the given problem.

Used formulae:-

→ The coordinates of the centroid of a triangle formed the three vertices is

G = ( (x1+x2+x3)/3 , (y1+y2+y3)/3 )

Answer 2

Answer:

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