Correct Answer – Option 3 : 12, -2

Concept:

The centroid of a Triangle: The point where the three medians of the triangle intersect.

Let’s consider a triangle. If the three vertices of the triangle are A(x1, y1), B(x2, y2), C(x3, y3)

The centroid of a triangle

=\(\rm (\frac{x_1+x_2+x_3}{3}, \frac{y_1+y_2+y_3}{3})\)

Calculation:

Here, vertices of triangle (4,x), (y,-5) and (7, 8) and Centroid = (3, 5)

So, 3 = \(\rm \frac{4+y+7}{3}\)

⇒11+y = 9 

⇒ y = -2

And, 5 = \(\rm \frac{x-5+8}{3}\)

⇒ x + 3 = 15

⇒ x = 12

∴ x = 12, and y = -2

Hence, option (3) is correct.