Question

If (7. -6), (2, k) and (h, 18) are the vertices of a triangle and
P(1,5) is the centroid, then find the values of h and k.
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Answer 1

Answer:

The value of h is 6

and the value of k is 3

Answer 2

h = - 6 and k = 3

Step-by-step explanation:

Here, ($x_{1}$ = 7, $y_{1}$ = - 6), ($x_{2}$ = 2, $y_{2}$ = k) and ($x_{3}$ = h, $y_{3}$ = 18)

To find, the values of h and k = ?

We know that,

The centroid of  triangle (x, y) = $\dfrac{x_{1}+x_{2}+x_{3}}{3}$, $\dfrac{y_{1}+y_{2}+y_{3}}{3}$

∴ $\dfrac{x_{1}+x_{2}+x_{3}}{3}$ = x

⇒ $\dfrac{7+2+h}{3}$ = 1

⇒ 9 + h = 3

⇒ h = 3 - 9 = - 6

Also,

$\dfrac{-6+k+18}{3}$ = 5

⇒ k + 12 = 15

⇒ k  = 15 - 12 = 3

∴  h = - 6 and k = 3