Exams › SSC CGL (Prelims) › General

A triangle has vertices at X(1,2), Y(4,6), and Z(-3,5). What is its area?

1. 10.5 square units
2. 12.5 square units
3. 11.5 square units
4. 14.5 square units

Correct answer: 12.5 square units

Solution

Using the area formula for coordinates, \(\frac12 |x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\), we get \(\frac12 |1(6-5)+4(5-2)+(-3)(2-6)|\). This becomes \(\frac12 |1+12+12| = \frac{25}{2} = 12.5\).

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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