Exams › SSC CGL (Prelims) › General

Triangle PQR has its centroid at \(G(2,-1)\), and vertex \(P\) is located at \((-4,5)\). If point \(M\) is the midpoint of side \(QR\), what are the coordinates of \(M\)?

1. (4, -3)
2. (5, -4)
3. (3, -2)
4. (6, -5)

Correct answer: (5, -4)

Solution

In a triangle, the centroid divides each median in the ratio \(2:1\) from the vertex. So for median \(PM\), \(G\) divides it such that \(G = \frac{2M+P}{3}\). Solving gives \(M=(5,-4)\).

Related SSC CGL (Prelims) General questions

• What is the equation of a line passing through \((0,4)\) with slope \(-2\)?
• What is the slope of the line perpendicular to $y = 5x - 8$?
• Which line has slope \(-2\) and passes through \((3,5)\)?
• A line \(L\) is the perpendicular bisector of the line segment joining points \(P(4,6)\) and \(Q(10,2)\). What is the y-intercept of line \(L\)?
• Find the slope of the line $4x - 5y = 10$.
• Find the equation of the perpendicular bisector of the line segment joining the points $(1,5)$ and $(5,9)$.

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