2018 Section C Question 15 A

Coordinate geometry question. Two key concepts tested:

1. Property of diagonals of a parallelogram. Applying the mid-point formula on this property

2. Computing length of a line segment joining two points

A medium difficulty 3-mark question. Exercise caution while computing values of 'a' and 'b' and the lengths of the sides.

Question 15A: A(-2, 1), B(a, 0), C(4, b) D(1, 2) are the vertices of a parallelogram ABCD. Find the values of a and b. Hence find the lengths of its sides.

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A(-2, 1), B(a, 0), C(4, b) and D(1, 2) are vertices of parallelogram.

**Key Property**: In a parallelogram, diagonals bisect each other.

The diagonals are AC and BD.

Essentially, the coordinates of mid-point of AC = coordinates of mid-point of BD.

(\\frac{-2 + 4}{2}), \\frac{1 + b}{2})) = (\\frac{a + 1}{2}), \\frac{0 + 2}{2}))

(2 , \\frac{1 + b}{2})) = (\\frac{a + 1}{2}), 1)

2 = \\frac{a + 1}{2}) and \\frac{1 + b}{2}) = 1

4 = a + 1 and 1 + b = 2

a = 3 and b = 1

Opposite sides of a parallelogram are equal. So, AB = CD and BC = AD.

Length of line segment joining points (x_{1}, y_{1}) and (x_{2}, y_{2}) is \\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\\)

Length of AB = \\sqrt{(1 - (-2))^2 + (0- 1)^2}\\) = \\sqrt{3^2 + 1^2}\\) = \\sqrt{10}\\)

Length of BC = \\sqrt{(4 - 1)^2 + (1 - 0)^2}\\) = \\sqrt{3^2 + 1^2}\\) = \\sqrt{10}\\)

**Note**: Because, AB = BC, the parallelogram is a __rhombus__.

Class 10 Maths

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CBSE Class 10 Maths - 2022

- Real Numbers Revision Class
- Polynomials Revision Videos
- Linear Equations Revision Class
- Quadratic Equations Revision Class
- Arithmetic Progressions Revision Video
- Triangles Revision
- Coordinate Geometry Revision
- Trigonometry Revision Class
- Appl of Trigonometry
- Circles Revision Class
- Areas Related to Circles Revision Videos

1. Section A | 2018 CBSE Class 10 Maths 1 Mark **Questions 1 to 6**

2. Section B | 2018 CBSE Class 10 Maths 2 Mark **Question 7** | Real Numbers - Irrational Numbers

3. Section B | 2018 CBSE Class 10 Maths 2 Mark **Question 8** | Linear Equations in 2 variables

4. Section B | 2018 CBSE Class 10 Maths 2 Mark **Question 9** | Sum of Arithmetic Progressions

5. Section B | 2018 CBSE Class 10 Maths 2 Mark **Question 10** | Coordinate Geometry Section Formula

6. Section B | 2018 CBSE Class 10 Maths 2 Mark **Question 11** | Probability of Rolling 2 dice

7. Section B | 2018 CBSE Class 10 Maths 2 Mark **Question 12** | Probability of selecting numbers

8. Section C | 2018 CBSE Class 10 Maths 3 Mark **Question 13** | Real Numbers - LCM & HCF

9. Section C | 2018 CBSE Class 10 Maths 3 Mark **Question 14** | Polynomial Factorization

10. Section C | 2018 CBSE Class 10 Maths 3 Mark **Question 15A** | Coordinate Geometry - Parallelogram

11. Section C | 2018 CBSE Class 10 Maths 3 Mark **Question 15B** | Coordinate Geometry - Area of Triangles

12. Section C | 2018 CBSE Class 10 Maths 3 Mark **Question 16** | Quadratic Equations - Speed Time Distance

13. Section C | 2018 CBSE Class 10 Maths 3 Mark **Question 17** | Similar & Congruent Triangles

14. Section C | 2018 CBSE Class 10 Maths 3 Mark **Question 19** | Trigonometric Ratios

15. Section C | 2018 CBSE Class 10 Maths 3 Mark **Question 20** | Areas related to circles - sector area

16. Section C | 2018 CBSE Class 10 Maths 3 Mark **Question 21** | Surface Areas & Volumes - Cylinder, hemisphere and cone

17. Section C | 2018 CBSE Class 10 Maths 3 Mark **Question 22** | Statistics - Median

18. Section D | 2018 CBSE Class 10 Maths 4 Mark **Question 23** | Quadratic Equations _ Speed Distance Time

19. Section D | 2018 CBSE Class 10 Maths 4 Mark **Question 24** | Arithmetic Progressions

20. Section D | 2018 CBSE Class 10 Maths 4 Mark **Question 25A** | Equilateral & Right Triangles and Congruence

21. Section D | 2018 CBSE Class 10 Maths 4 Mark **Question 25B** | Pythagoram Theorem Proof

22. Section D | 2018 CBSE Class 10 Maths 4 Mark **Question 27** | Trigonometric Ratios & Identities

23. Section D | 2018 CBSE Class 10 Maths 4 Mark **Question 28** | Surface Area of Frustum

24. Section D | 2018 CBSE Class 10 Maths 4 Mark **Question 29** | Applications of Trigonometry - Heights & Distances

25. Section D | 2018 CBSE Class 10 Maths 4 Mark **Question 30** | Statistics - 2 Alternatives

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