Practice the questions given in the worksheet on collinearity of three points. We know that in general, P, Q and R are collinear if the sum of the lengths of any two line segments among PQ, QR and RP is equal to the length of the remaining line segment, that is, either PQ + QR = PR or PR + RQ = PQ or QP + PR = QR

**1.** Prove that the points (4, -5) and (1, 1) and (-2, 7) are collinear.

**2.** Show that the following points are collinear:

(i) P(1, 1), Q(-2, 7) and R(3, -3)

(ii) P(2, 0), Q(11, 6) and R(-4, -4)

**3.** Prove that the points (a, b + c) and (b, c + a) and (c, a
+ b) are collinear, where a > b > c.

**4.** Using the distance formula show that the points A(6, 9),
B(0, 1) and C(-6, -7) are collinear.

**5.** For what value of k, the points (k, -2), (1, 4) and (-3,
16) in given order are collinear?

**6.** Show that the points A(-1, -1), B(2, 3) and C(8, 11) are
collinear.

**7.** Prove the points (2, 3), (-4, -6) and (1, 3/2) cannot be
the three vertices of a triangle.

**8.** By distance formula, show that the points (1, -1), (5, 2)
and (9, 5) are collinear.

**Answer:**

Answer for the worksheet on collinearity of three points are given below:

**5.** 3

● **Distance and Section Formulae**

**Distance Formula****Distance Properties in some Geometrical Figures****Conditions of Collinearity of Three Points****Problems on Distance Formula****Distance of a Point from the Origin****Distance Formula in Geometry****Section Formula****Midpoint Formula****Centroid of a Triangle****Worksheet on Distance Formula****Worksheet on Collinearity of Three Points****Worksheet on Finding the Centroid of a Triangle****Worksheet on Section Formula**

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