WORKSHEET-1 OF COORDINATE GEOMETRY CLASS-10

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1.  Find the distance between points A(2, 3) and B(4, 5).

2. Find the distance between points C(-1, 2) and D(3, -4).

3. Find the distance between points E(2, 2) and F(4, 4).

4. Find the distance between points G(1, 1) and H(2, 3).

5. Find the distance between points I(-2, -3) and J(4, 5).

6. Find x if d = 5, (x, 2) and (3, 4) are the coordinates of the two points.

7. If d = 7, find x in (x, 1) and (2, 3).

8. Given d = 10, find x in (x, 2) and (4, 5).

9. Find x if d = 12, (x, 3) and (1, 4) are the coordinates of the two points.

10. If d = 15, find x in (x, 2) and (3, 5).

11. Given d = 20, find x in (x, 1) and (2, 4).

12. Find x if d = 25, (x, 3) and (2, 5) are the coordinates of the two points.

13. If d = 30, find x in (x, 2) and (4, 6).

14. Given d = 35, find x in (x, 1) and (3, 5).

15. Find x if d = 40, (x, 3) and (2, 6) are the coordinates of the two points.

16. Find the midpoint of the line segment joining the points (2, 3) and (4, 5).

17. If the coordinates of two points are (x1, y1) = (1, 2) and (x2, y2) = (3, 4), find the midpoint of the line segment joining them.

18. Find the midpoint of the line segment joining the points (-1, 2) and (3, -4).

19. If the midpoint of a line segment is (2, 3) and one of the endpoints is (1, 2), find the other endpoint.

20. Find the midpoint of the line segment joining the points (2, 2) and (4, 4).

21. Find the distance from the origin to the point (3, 4).

22. If the coordinates of a point are (x, y) = (2, -3), find the distance from the origin to this point.

23. Find the distance from the origin to the point (-2, 5).

24. If the coordinates of a point are (x, y) = (-1, 2), find the distance from the origin to this point.

25. Find the distance from the origin to the point (4, -2).

26. Find the coordinates of the point that divides the line segment joining the points (2, 3) and (4, 5) in the ratio 2:3.

27. If the coordinates of two points are (x1, y1) = (1, 2) and (x2, y2) = (3, 4), find the coordinates of the point that divides the line segment joining them in the ratio 3:4.

28. Find the coordinates of the point that divides the line segment joining the points (-1, 2) and (3, -4) in the ratio 3:2.

29. If the coordinates of two points are (x1, y1) = (2, 3) and (x2, y2) = (4, 5), find the coordinates of the midpoint of the line segment joining them.

30. Find the coordinates of the point that divides the line segment joining the points (2, 2) and (4, 4) in the ratio 1:2.

31. Find the ratio in which the point (2, 3) divides the line segment joining the points (1, 2) and (3, 4).

32. If the point (x, y) = (4, 5) divides the line segment joining the points (2, 3) and (6, 7) in the ratio m:n, find the values of m and n.

33. Find the ratio in which the point (-1, 2) divides the line segment joining the points (-3, 1) and (2, 4).

34. If the point (x, y) = (3, 4) divides the line segment joining the points (1, 2) and (5, 6) in the ratio 2:3, verify the section formula.

35. Find the ratio in which the point (2, 2) divides the line segment joining the points (1, 1) and (3, 3).

36. Prove that the points (2, 3), (4, 5), and (6, 7) form a triangle.

37. Show that the points (1, 2), (3, 2), (3, 4), and (1, 4) form a square.

38. Prove that the points (2, 3), (6, 3), (6, 5), and (2, 5) form a rectangle.

39. Prove that the points (3, 4), (5, 4), (5, 6), and (3, 6) form a parallelogram.

40. Show that the points (1, 1), (2, 1), (2, 2), and (1, 2) form a rhombus.

41. Prove that the points (2, 3), (4, 5), and (6, 7) form an isosceles triangle.

42. Verify that the points (1, 2), (3, 2), (3, 4), and (1, 4) form a rectangle.

43. Prove that the points (2, 3), (4, 5), and.           (6, 7) form a scalene triangle.

44. Find the area of the triangle with vertices (2, 3), (4, 5), and (6, 7).

45. Find the area of the triangle with vertices (1, 2), (3, 4), and (5, 6).

46. Find the area of the triangle with vertices (-1, 2), (2, 5), and (4, 1).

47. Find the area of the triangle with vertices (3, 4), (6, 7), and (9, 10).

48. Find the area of the triangle with vertices (2, 3), (5, 6), and (8, 9).

49. Find the area of the triangle with vertices (-2, -3), (1, 2), and (4, 5).

50. Find the area of the triangle with vertices (1, 1), (3, 3), and (5, 5).

CONCEPT OF CO-ORDINATE GEOMETRY OF CLASS-10

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Co-ordinate geometry tell us the location of a point on a plane .

the coordinates of a point are (x, y), 

where x-coordinate (abscissa) denotes the distance of a point from the y-axis 

and y-coordinate (ordinate denotes the distance of the point from the x-axis

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Required conditions for a triangle:

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  A triangle has three sides. The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
• AB + BC = AC

CONCEPT OF STRAIGHT LINE OF CLASS-11

All Formulas of Coordinate Geometry.
Coordinate of  origin	O (0,0)
Equation of x-axis	y = 0
Equation of y-axis	x = 0
Equation parallel to x-axis	y = ± k
Equation parallel to y-axis	x = ± k
The slope of a Line Using Coordinates	m = Δy/Δx     = (y2 − y1)/(x2 − x1)
The slope of a Line Using General Equation Ax + By + c = 0	m =  - { A / B }
The slope of a Line using angle (θ)	m = tanθ
For parallel Lines	m1 = m2
For Perpendicular Lines,	m1.m2 = -1
General Form of a Line	Ax + By + C = 0
Slope , Intercept of  y-axis Form of a Line	y = mx + c
Slope , Intercept of  x-axis Form of a Line	y = m(x - d )

Intercept-Intercept Form	x/a + y/b = 1
Perpendicular from	x cos α + y sin α = a
Point-Slope Form	y − y1= m(x − x1)
If two points are given	y − y1=[ (y2 − y1)/(x2 − x1) ]  (x − x1)
Midpoint Formula	M (x, y) = [(x1 + x2) /2, (y1 + y2) /2 ]
Angle Formula	tan θ = [(m1 – m2)/ 1 + m1m2]
Area of a Triangle Formula	1/2[|x1(y2−y3)+x2(y3–y1)+x3(y1–y2)| ]
Distance from a Point to a Line	d = [|Ax1 + By1 + C| / √(A2 + B2)]

Distance from origin to a Line	d = [| C| / √(A2 + B2)]
Section Formula (Internal division)	P(x, y) = [(m1x2 + m2x1)/(m1 + m2), (m1y2 + m2y1)/(m1 + m2)]
Section Formula (External division)	P(x, y) = [(m1x2 – m2x1)/(m1 – m2), (m1y2 – m2y1)/(m1 – m2)]