Exercise 7.1

1. Find the distance between the following pairs of points:

(i) (2, 3), (4, 1)

(ii) (-5, 7), (-1, 3)

Solution:

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(iii) (a, b), (- a, – b)

Solution:

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2. Find the distance between the points (0, 0) and (36, 15). Can you now find the distance between the two towns, A and B, discussed in Section 7.2?

Solution:

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3. Determine if the points (1, 5), (2, 3) and (-2, -11) are collinear.

Solution:

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4. Check whether (5, – 2), (6, 4) and (7, – 2) are the vertices of an isosceles triangle.

Solution:

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5. In a classroom, 4 friends are seated at points A, B, C and D, as shown in Fig. 7.8. Champa and Chameli walk into the class, and after observing for a few minutes, Champa asks Chameli, “Don’t you think ABCD is a square?” Chameli disagrees. Using the distance formula, find which of them is correct.

Solution:

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6. Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer:

(i) (- 1, – 2), (1, 0), (- 1, 2), (- 3, 0)

Solution:

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(ii) (- 3, 5), (3, 1), (0, 3), (- 1, – 4)

Solution:

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(iii) (4, 5), (7, 6), (4, 3), (1, 2)

Solution:

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7. Find the point on the x-axis which is equidistant from (2, – 5) and (- 2, 9).

Solution:

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8. Find the values of y for which the distance between the points P (2, – 3) and Q (10, y) is 10 units.

Solution:

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9. If Q (0, 1) is equidistant from P (5, – 3) and R (x, 6), find the values of x. Also, find the distance QR and PR.

Solution:

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10. Find a relation between x and y such that the point (x, y) is equidistant from the point (3, 6) and (- 3, 4).

Solution:

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