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
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