Question

the vertices of a triangle are ( 1,2),(h,-3)and(-4,k).if the centroid of the triangle is atbthe point(5,-1) then find the value of root of(h+k)^2+(h+3k)^2

Answer 1

Answer:

3088

Step-by-step explanation:

The centroid (x, y) of a triangle can be determined by:

$x=\frac{x_{1}+x_{2}+x_{3}}{3},\ \ \ \ \ \ y=\frac{y_{1}+y_{2}+y_{3}}{3}$

So, here We have centroid (5, -1),

Thus, $5=\frac{1+h-4}{3},\ \ \ \ \ \ -1=\frac{2-3+k}{3}$

⇒ h = 18 and k = 10

Now, for finding the value of root of (h + k )² + (h + 3k)²

⇒ (18 + 10)² + (18 + 30)² = 3088