position on a map. Line - an unlimited number of points along the same path. The set of points may be straight or form a curve. Normally‚ the term ’line’ means a straight line. The ’line’ has no dimensions (length‚ width‚ height) and extends unlimited in both directions. (The part of a line defined by two points‚ called ’endpoints’‚ is call a line segment or ’segment’.) A ’line’ is represented by a drawn line with arrowheads on each end to represent that it doesn’t have endpoints. A line can be named in
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CLASS - XI MATHEMATICS (Straight Line) 1. 2. Find the distance of the point ( 2‚3) from the line 12 x − 5 y = 2 Find the equation of a line whose perpendicular distance from the origin is 5 units and angle between the positive direction of the x -axis and the perpendicular is 300. [1] [1] 3. 1 Write the equation of the lines for which tan θ = ‚ where Q is the inclination 2 of the line and x intercept is 4. Find the Angle between the x -axis and the line joining the points ( 3‚ −1) and
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paint styles‚ using a selected state or snapshot. Magic Eraser Tool: erases pixels and restores parts of an image to a previously saved state. Background Eraser Tool: erases areas to transparency by dragging. Gradient Tool: create straight-line‚ radial *‚ angle *‚ reflected *‚ and diamond *‚ blends between colors. Paint Bucket Tool: fills similarly colored areas with the foreground color. Blur Tool: blurs hard edges in an image. Sharpen Tool: sharpens soft edges in an image. Smudge
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origin O and axis lines X‚ Y and Z‚ oriented as shown by the arrows. The tick marks on the axes are one length unit apart. The black dot shows the point with coordinatesX = 2‚ Y = 3‚ and Z = 4‚ or (2‚3‚4). Choosing a Cartesian coordinate system for a three-dimensional space means choosing an ordered triplet of lines (axes)‚ any two of them being perpendicular; a single unit of length for all three axes; and an orientation for each axis. As in the two-dimensional case‚ each axis becomes a number line. The coordinates
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or lying on the same staright line. Coplanar is lying on or occurring in the same plane. Define Non-Collinear Points The points which do not lie on the same line are known as Non-Collinear Points Below diagram represent‚ Non-Collinear Points P‚ Q‚ R & S. In the above Diagram‚ Points P‚ Q‚ R & S doesn not falls on the same line and Hence they are called Non-Collinear Points. | Coplanar Definition of Coplanar * A set of points‚ lines‚ line segments‚ rays or any other geometrical
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median is 5 and the mean is 7. Find (a) (b) (c) x; y; z. –4– [1 mark] [2 marks] [3 marks] M12/5/MATSD/SP1/ENG/TZ1/XX 2. 2.Working: The coordinates of point A are (−4 ‚ p ) and the coordinates of point B are (2 ‚ − 3) . The mid-point of the line segment AB‚ has coordinates (q ‚ 1) . (a) Find the value of (i) (ii) (b) q; p. [4 marks] [2 marks] Calculate the distance AB. 3. –5– M12/5/MATSD/SP1/ENG/TZ1/XX Working: is a star that is 82 414 080 000 000 km away from Earth. A spacecraft
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machine and lathe-bed guide ways. Straightness is defined as ’’A condition in which an element of a surface or an axis is a straight line’’. Flatness is said to exist if the following conditions are satisfied: 1) ’’all generators (lines) must be straight’’ and/or 2) ’’all generators (lines) must lie in the same plane’’. [pic] Fig. 2.1 A surface‚ all of whose generators (lines) parallel to the sides are straight‚ but which is not flat There are several ways with which the straightness and flatness of
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rate. [3] (b) (c) If (x - 2) is a factor of 2 x3- x2- px-2 (i) find the value of p. (ii) with the value of p‚ factorize the above expression completely.[4] Question 2 (a) Solve the given inequation and graph the solution on the number line. (b) In the given figure‚ find the area of the unshaded portion within the rectangle. [3] (c) A shopkeeper buys a camera at a discount of 20% from the wholesaler‚ the printed price of the camera being Rs.1600 and the rate of sales tax is 6%
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coordinates of the points Q and R on medians BE and CF respectively such that BQ : QE = 2 : 1 and CR : RF = 2 : 1. Q. 11. In what ratio does the line 4x + y = 11 divide the line segment joining the points (1‚ 3) and (2‚ 7). Q. 12. If the points (5‚ 4) and (x‚ y) are equidistant from the point (4‚ 5); then show that x2 + y2 – 8x – 10y + 39 = 0 Q. 13. The line segment joining the points (3‚ – 4) and (1‚ 2) is trisected at the points P and Q. If the coordinates of P and Q are (p‚ – 2) and (5/3‚ q) respectively
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method for finding geometric structures in digital images is proposed. An adaptive algorithm of straight line segments extraction is developed for manmade objects description in digital images. It uses an adjustment of oriented filter angle for precise extraction of line corresponding to real edge. Perceptual grouping approach is applied to these segments to obtain simple and complex structures of lines on the base of their crossings. Initial image is presented as a collection of closed structures with
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