JEE Mains · Maths · STD 11 - 9. straight line
A point \(P\) moves on the line \(2x -3y + 4 = 0\). If \(Q(1, 4)\) and \(R(3, -2)\) are fixed points, then the locus of the centroid of \(\Delta PQR\) is a line
- A with slope \(\frac{3}{2}\)
- B parallel to \(x-\) axis
- C with slope \(\frac{2}{3}\)
- D parallel to \(y-\) axis
Answer & Solution
Correct Answer
(C) with slope \(\frac{2}{3}\)
Step-by-step Solution
Detailed explanation
Let point \(P\) is \(\left( {\alpha ,\beta } \right)\,\) and center of \(\Delta PQR\) is \((h,k)\), then \(3h = \alpha + 1 + 3\,\,\) and \(3k = \beta + 4 - 2\) \( \Rightarrow \alpha = 3h - 4\) and \(\beta = 3k - 2\) Because \(\left( {\alpha ,\beta } \right)\) lies on…
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