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**Q.1. Find the distance between the following pairs of points:****(i) (2, 3), (4, 1) ****(ii) (-5, 7), (-1, 3) ****(iii) (a, b), (-a, -b)****Sol. **(i) Let A(2, 3) and B(4, 1)

The distance between two points is

(ii) Let A (-5, 7) and B (-1, 3)

(iii) Let A (a, b) and B (-a, -b)**Q.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?****Sol. **Let points be A (0, 0) and B (36, 15)

The distance between two points is**Q.3. Determine if the points (1, 5), (2, 3) and (-2, -11) are collinear.****Sol.** Let points be A(1, 5), B(2, 3) and C(-2, -11)

AB + BC â‰ AC

Hence, the given points are not collinear.**Q.4. Check whether (5, -2), (6, 4) and (7, -2) are the vertices of an isosceles triangle.****Sol.** Let the points be A (5, -2), B (6, 4) and C (7, -2).

Here AB = BC

âˆ´ Î” ABC is an isosceles.**Q.5. In a classroom, 4 friends are seated at the points A, B, C and D as shown in Fig. Champa and Chameli walk into the class and after observing for a few minutes Champa asks Chameli, â€˜â€˜Donâ€™t you think ABCD is a square?â€™â€™ Chameli disagrees. Using distance single formula, find which of them is correct.****Sol.** Points A (3, 4), B (6, 7), C (9, 4) and D (6, 1)

âˆ´ ABCD is a square.

Hence, Champa is correct.**Q.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)****(ii) (-3, 5), (3, 1), (0, 3), (-1, - 4)****(iii) (4, 5), (7, 6), (4, 3), (1, 2)****Sol.** (i) Let the points be: A (-1, -2), B (1, 0), C (-1, 2) and D (-3, 0).

The distance between two points is

Here AC - BD, AB = BC = CD = AD

Hence, the quadrilateral ABCD is a square.

(ii) Let points be A (-3, 5), B (3, 1), C (0, 3) and D (-1, -4)

The given points do not form any quadrilateral.

(iii) Let points be A (4, 5), B (7, 6), C (4, 3) and D (1, 2)

Here, AB = CD, BC = AD and AC â‰ BD

âˆ´ The quadrilateral ABCD is a parallelogram.**Q.7. Find the point on the x-axis which is equidistant from (2, -5) and (-2, 9).****Sol.** Let points be A (2, -5) and B (-2, 9)

Let P (x, 0) be the point on x-axis.

âˆ´ PA = PB**Q.8. Find the values of y for which the distance between the points P(2, -3) and Q(10, y) is 10 units.****Sol.** Points P (2, -3), Q (10, y) and PQ = 10 units

The distance between two points is

â‡’ y - 3 = 0 or y + 9 = 0

â‡’ y = 3 or - 9**Q.9. If Q (0, 1) is equidistant from P (5, -3) and R (x, 6), find the values of x. Also, find the distances QR and PR.****Sol.** PQ = QR

Therefore, point R is (4, 6) or (âˆ’4, 6).

When point R is (4, 6),**Q.10. Find a relation between x and y such that the point (x, y) is equidistant from the point (3, 6) and (-3, 4).****Sol. **Points A (3 , 6), B (-3, 4) and point P(x, y) is equidistant from points A and B

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