- Flash Back from Class IX notes
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- Distance formula
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- Section Formula
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- Area of triangle
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- How to Solve the line segment bisection ,trisection and four-section problem's
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- How to Prove three points are collinear
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- How to solve general Problems of Area in Coordinate geometry

- Coordinate Geometry Problem and Solutions
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- Coordinate Geometry Short questions
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- Coordinate Geometry 3 Marks Questions
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- Coordinate Geometry 5 Marks questions

Given below are the **Class 10 Maths** Important Questions(3 Marks questions) for Coordinate Geometry

b) Calculation problems

c) Multiple choice questions

d) Long answer questions

e) Fill in the blank's

- Find the centre of the circle passing through (6, -6), (3, -7) and (3, 3)
- Two opposite vertices of a square are (-1, 2) and (3, 2). Find thee co-ordinates of other two vertices.
- Prove that the points (3, 0), (4, 5), (-1, 4) and (-2, -1), taken in order, form a rhombus. Also, find its area.
- Find a point on y – axis which is equidistant from the points (5, -2) and (-3, 2).
- Find a relation between a and b such that the point (a, b) is equidistant from the points (3, 6) and (-3, 4).
- If the coordinates of the mid points of the sides of a triangle are (1, 2), (0, -1) and (2, -1). Find the coordinates of its vertices.
- The coordinates of one end point of a diameter of a circle are (4, -1) and the co-ordinates of the centre of the circle are (1, -3). Find the co- ordinates of the other end of the diameter.
- If A (5, -1), B (-3, -2) and C (-1, 8) are the varieties of triangle ABC, find the length of median through A and the co- ordinates of the centroid.
- If the mid- point of the line joining (3, 4) and (z, 7) is (x, y) and 2x + 2y + 1 = 0 find the value of z.
- Find the ratio in which the line segment joining (-2, -3) and (5, 6) is divided by (i) x – axis (ii) y –axis. Also, find the co- ordinates of the point of division in each case.
- Prove that (4, 3), (6, 4), (5, 6) and (3, 5) are the angular points of a square.
- Three vertices of a parallelogram are (a +b, a – b), (2a + b, 2a – b), (a – b, a + b).Find the fourth vertex.
- If two vertices of a parallelogram are (3, 2), (-1, 0) and the diagonals cut at (2, -5), find the other vertices of the parallelogram.
- Find the lengths of the medians of a
**Δ**ABC having vertices at A (0, -1), B (2, 1) and C (0, 3). - Find the lengths of the medians of a
**Δ**A (5, 1), B (1, 5) and C (-3, -1). - Find the co- ordinates of the points which divide the line segment joining the points (-4, 0) and (0, 6) in four equal parts.
- Show that following points are vertices of a rectangle:

(a) (2 , –2) , ( 8, 4) , ( 5, 7 ) , (– 1, 1)

(b)(–4 , –1) , (–2 , 4) , ( 4, 0 ) , ( 2, 3 )

18. If centre of circle passing through (a,–8), (b,–9) and (2,1) is (2,–4), find the value of a and b.

**Answer**

1. (3, -2)

2. (1, 0) and (1, 4)

3. Area = 24 sq. units

4. (0, -2)

5. 3a + b = 5

6. (1, -4), (3, 2), (-1, 2)

7. Co- ordinates are (-2, -5)

8. Median = **√65** units, co- ordinate = [ 1/3,5/3 ]

9. z =-15

10 (i) 1 : 2; [1/3,0]

(ii) 2 : 5; [ 0, -3/7 ]

12. (-b, b)

13. (1, -12), (5, -10)

14. AD = **√**10 units, BE = 2units, CF = **√**10 units

15. AD = **√**37 units, BE = 5 units, CF = 2 **√**13 units

16. (-3, 1.5), (-2, 3), (-1, 4.5)

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