Exams › SSC CGL (Prelims) › General

In a triangle with vertices \(A(x,y)\), \(B(6,-2)\), and \(C(3,8)\), the centroid is at \(G(5,3)\). What are the coordinates of vertex \(A\)?

1. (5, 2)
2. (6, 3)
3. (7, 4)
4. (8, 5)

Correct answer: (6, 3)

Solution

The centroid of a triangle is \(\left(\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3}\right)\). Using \(G(5,3)\) with \(B(6,-2)\) and \(C(3,8)\), we get \(x+6+3=15\Rightarrow x=6\) and \(y-2+8=9\Rightarrow y=3\). So \(A=(6,3)\).

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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