If centroid of triangle with vertices (4, p), (-1, -1) and (3, 5)  is given by the mid-point of (1, 4) & (q, 2), then p² + q² will be:

Given: 

Vertices of triangle are (4, p), (-1, -1) and (3, 5)

Concept:

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 = 

Mid-point: If two points are (x₁, y₁) and (x₂, y₂), then mid point is given by

Calculation:

We know that, centroid of triangle is given by 

G = 

Therefore, for given triangle, we will get centroid 

G = 

According to question, G is the mid-point of (1, 4) & (q, 2). Therefore, by using mid-point formula

On comparing both side

⇒ q = 3 & q = 5

⇒ p² + q² = 34

Hence, option 4 is correct.