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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 P(2, 3) and Q(4, 1)

**(ii)** Let P (-5, 7) and Q (-1, 3)**(iii)** Let P (a, b) and Q (-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 ≠ 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

∴ Δ 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, ‘‘Don’t you think ABCD is a square?’’ 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)

**∴** 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).

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 ≠ BD****∴** 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 the x-axis.

**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:__

⇒ y - 3 = 0 or y + 9 = 0

⇒

When point R is (4, 6),

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