Maths : Coordinate Geometry: Book Back, Exercise, Example Numerical Question with Answers, Solution: Exercise 5.2: Distance between any Two Points

**Coordinate Geometry: Distance between any Two
Points**

**Exercise 5.2**

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

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

**(ii) (3,4) and (– 7, 2)**

**(ii) (a, b) and (c, b)**

**(iv) (3,– 9) and (–2, 3)**

**2. Determine whether the given set of
points in each case are collinear or not.**

**(i) (7,–2),(5,1),(3,4)**** ****(ii) ( a,–2), (a,3), (a,0)**

**3. Show that the following points taken
in order form an isosceles triangle.**

**(i)****
***A ***(5,4), B(2,0), C (–2,3)**

**4. Show that the following points taken
in order form an equilateral triangle in each case.**

**(i) A(2, 2), B(–2, –2), C( -2√3 , 2√3
) (ii) A(√3 , 2) , B (0,1), C(0,3)**

**5. Show that the following points taken
in order form the vertices of a parallelogram.**

**(i)****
***A***(–3, 1), B(–6, –7), C (3,
–9), D(6, –1)**

**6. Verify that the following points taken
in order form the vertices of a rhombus.**

**(i)****
***A***(3,–2), B (7,6),C (–1,2),
D (–5, –6)**

**7. A **

**8. The abscissa of a point A is
equal to its ordinate, and its distance from the point B(1, 3) is 10 units,
What are the coordinates of A?**

**9. The point ( x, y) is equidistant
from the points (3,4)and(–5,6). Find a relation between x and y.**

**10. Let A(2, 3) and B(2,–4)
be two points. If P lies on the x-axis, such that AP = 3/7 AB,
find the coordinates of P.**

**11. Show that the point (11,2) is the
centre of the circle passing through the points (1,2), (3,–4) and (5,–6)**

**12. The radius of a circle with centre
at origin is 30 units. Write the coordinates of the points where the circle intersects
the axes. Find the distance between any two such points.**

Tags : Numerical Problems with Answers, Solution | Coordinate Geometry | Maths , 9th Maths : UNIT 5 : Coordinate Geometry

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9th Maths : UNIT 5 : Coordinate Geometry : Exercise 5.2: Distance between any Two Points | Numerical Problems with Answers, Solution | Coordinate Geometry | Maths

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