##### Chapter

#### Coordinate Geometry

#### EXERCISE

##### Type - 1

###### Question 1 :

Find the smallest number by which each of the following numbers must be multiplied to obtain a perfect cube.

(i) 243

(ii) 256

(iii) 72

(iv) 675

###### Formulae used :

Distance Formula to find distance between two points (x_{1},y_{1}) and (x_{2},y_{2}) is : **D = √[(x _{2} – x_{1})^{2} + (y_{2} – y_{1})^{2} ]**.

###### Solution :

(i) We have 243 = 3 × 3 × 3 × 3 × 3

The prime factor 3 is not a group of three.

∴ 243 is not a perfect cube.

Now, [243] × 3 = [3 × 3 × 3 × 3 × 3] × 3

or 729 =3 × 3 × 3 × 3 × 3 × 3

Now, 729 becomes a perfect cube.

Thus, the smallest required number to multiply 243 to make it a perfect cube is 3.

##### Class Work

**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)

**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)

**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)

##### Answer

(i) 5 m

(i) 5 m

(i) 5 m

##### Assignment

**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)

##### Answer

(i) 5 m

(i) 5 m

(i) 5 m

##### NCERT Questions

Q1. Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and their coefficients:

(i) x

(ii) 4s

(iii) 6x

(iv) 4u

(v) t

(vi) 3x

(i) x

^{2}– 2x – 8(ii) 4s

^{2}– 4s + 1(iii) 6x

^{2}– 3 – 7x(iv) 4u

^{2}+ 8u(v) t

^{2}– 15(vi) 3x

^{2}– x – 4##### Answer

(i) 5 m

(i) 5 m

(i) 5 m

##### CBSE Questions

**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)

##### Answer

(i) 5 m

(i) 5 m

(i) 5 m

###### Related Topics

- Chapter 1 The Cell – Its Structure and Functions
- Chapter 2 Microorganisms: Friends or Foes
- Chapter 3 Metals and Non-Metals
- Chapter 4 Force and Pressure
- Chapter 5 Friction
- Chapter 6 Sources of Energy
- Chapter 7 Combustion
- Chapter 8 Conservation of Plants and Animals
- Chapter 9 Crop Production and Its Management
- Chapter 10 Refraction and Dispersion of Light
- Chapter 11 The Human Eye
- Chapter 12 Sound
- Chapter 13 Synthetic Fibres and Plastics
- Chapter 14 Reproduction in Animals
- Chapter 15 Reaching the Age of Adolescence
- Chapter 16 Electric Current and Its Chemical Effects
- Chapter 17 Stars and Solar System
- Chapter 18 Earthquakes
- Chapter 19 Pollution of Air
- Chapter 20 Pollution of Water