If the vertices `Pa n dQ` of a triangle `P Q R` are given by (2, 5) and `(4,-11)` , respectively, and the point `R` moves along the line `N` given by `9x+7y+4=0` , then the locus of the centroid of triangle `P Q R` is a straight line parallel to PQ (b) QR (c) RP (d) N

Explanation

To solve the problem step by step, we need to find the locus of the centroid of triangle PQR as point R moves along the line \( N: 9x + 7y + 4 = 0 \).

### Step 1: Identify the coordinates of points P and Q
The coordinates of point \( P \) are \( (2, 5) \) and the coordinates of point \( Q \) are \( (4, -11) \).

### Step 2: Parameterize the point R
Since point \( R \) moves along the line \( N: 9x + 7y + 4 = 0 \), we can express the coordinates of \( R \) in terms of a parameter \( h \) (which represents the x-coordinate of R).

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