Q49 of 59 Page 178

State whether the statements are true or false.

The points A (– 2, 1), B (0, 5), C (– 1, 2) are collinear.

Given points are A (– 2, 1), B (0, 5) and C (– 1, 2)

To prove: A (– 2, 1), B (0, 5) and C (– 1, 2) are collinear


Proof: Two ways to find that given points are collinear or not:


Ist way: If three points are collinear, then slope of any two pairs of points will be equal.


IInd way: If the value of area of triangle formed by the three points is zero, then the points are collinear.


So, we check by the 1st method


Slope of AB




Slope of BC



Slope of CA



Since, the slopes are different. So, the given points are not collinear.


Hence, the given statement is FALSE


More from this chapter

All 59 →
47

Fill in the blanks

Locus of the mid-points of the portion of the line x sin θ + y cos θ = p intercepted between the axes is ____.

 48

State whether the statements are true or false.

If the vertices of a triangle have integral coordinates, then the triangle can’t be equilateral.

 50

State whether the statements are true or false.

Equation of the line passing through the point (a cos3θ, a sin3θ) and perpendicular to the line x sec θ + y cosec θ = a is x cos θ – y sin θ = a sin 2θ.

 51

State whether the statements are true or false.

The straight line 5x + 4y = 0 passes through the point of intersection of the straight lines x + 2y – 10 = 0 and 2x + y + 5 = 0.