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Geometry-Coordinate

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Published in: Mathematics
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Coordinate Geometry.

Study P / Ranchi

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  1. CARTESIAN CO-ORDINATE SYSTEM : Rectangular Co-ordinate System : Let X' OX and Y 'OY be two mutually perpendicular lines through any point O in the plane of the pa- per. Point O is known as the origin. The line X'OX is called the x -axis or axis of x ; the line Y 'OY is known as the y-axis or axis of y, and the two lines taken together are called the co-ordinates axes or the axes of co-ordi- nates. Quadrant X' Ill Quadrant Quad- Region 3 2 Quadrant 1 -1 x -2 Quadrant -3 Y' Signs of Nature of X co-ordin- and Y ate XOY YOX' X'OY' Y'OX rant 1 11 111 IV Note - Any point lying on x-axis or y-axis does not lie in any quadrant. Any point can be represented on the plane described by the co-ordinate axes by specifr- ing its x and y co-ordinates. The x -co-ordinate of the point is also l«lown as the abscissa while the y-coordinate is also known as the ordinate. Distance Formula : The distance two point A (XP Yl) and B(X2, Y2) is given by 1
  2. N/A
  3. Area of the triangle formed by co-ordinate axes and the line a x + b y + c = O is 3
  4. origin to the line ax + by + c = O is given by 4
  5. 5
  6. 4) is . 13. The equation of a line with slope 5 and passing through the point (—4, 1) is . (a) y = 5x+ 21 (b) y = 5x— 21 (c) 5y = x + 21 (d) 5y = x— 21 14. The value of a so that the lines x + 3y —8 = O and ax + 12y + 5 = O are parallel is : 15. The value of P for which the lines 3x + 8y + O and 24 x + py + 19 9 O are perpendicualar is . (a) -12 (c) - 11 16. The value of a so that line joining P(—2, 5) and Q (O, —7) and the line joining A (—4, —2) and B(8, a) are perpendicular to each other is . 17. The angle between the lines represented by the equations 2y 6
  7. Hints and Solutions : LEVEL - 1 1. 2. 3. (b) The point (—5, 7) lies in the second quad- rant. (d) The point (7, —5) lies in the fourth quad- rant. (a) Distance between two points 7
  8. 23. (a) The slope of the line is 8
  9. 14. (c) Condition of parallelism 9
  10. ??
  11. Similarly, 11

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