Three vertices of a triangle are (h,5),(-4,k),(8,9).
If co-ordinates of the centroid is (-2,6) then find the value of h and k.
Answers
Solution :-
Here, Three vertices of a triangle are
( h, 5 ) , ( -4 , k) and ( 8 , 9 )
Compare these three vertices of a triangle with
(x1 , y1) , ( x2 , y2 ) and ( x3, y3 )
Here, The coordinates of the centroid is
( -2,6 )
Compare these with ( x, y )
By using the centroid ,
x = x1 + x2 + x3 / 3
Put the required values,
-2 = h + ( - 4) + 8 / 3
-2 = h - 4 + 8 / 3
-2 * 3 = h - 4 + 8
-6 = h + 4
h = -6 - 4
h = -10
Now,
y = y1 + y2 + y3 / 3
Put the required values,
6 = 5 + k + 9 / 3
6 * 3 = 5 + k + 9
18 = 14 + k
k = 18 - 14
k = 4
Hence, The value of h and k is
(-10 ) and 4
Here this is a question from coordinate geometry where we are given coordinates of a triangle and it's centroid. But the major problem is that the coordinates of triangle also have terms h and k, we have to find value of these variables. We can use formula for coordinates of centroid of triangle to find h and k.
So let's start!!
Given coordinates of centroid of ∆:
• (-2,6)
We have given vertices of ∆:
• A(h,5)
• B(-4,k)
• C(8,9)
Here value of :-
• X1=h
• X2=-4
• X3=8
• Y1=5
• Y2=k
• Y3=9
[You can take these values in any order]
We have formula for centroid of ∆:
Now put given values!
_____________________________
Now compare these coordinates!
Firstly we are comparing absicca (value of x axis).
Now cross multiply!
Now solve it by using transportation method for LHS & RHS.
Now compare ordinate (value of y axis).
Now cross multiply!
Now transport 14 from RHS to LHS!
So the required values of k and h are 4 and -10 respectively.
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