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COORDINATES, POINTS AND LINES

COORDINATES, POINTS AND LINES. Name : _______________ Class : 10 ___ Day/date : _______________. point. Point can be determined location, but do not have the size (magnitude) / dimensionless example:. . P. . A. point A. point P. ray AB. B.

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COORDINATES, POINTS AND LINES

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  1. COORDINATES, POINTS AND LINES Name : _______________ Class : 10 ___ Day/date : _______________ S1/W2/HO-1/G.11/Math/RIT-AYA/2010-2011

  2. point Point can be determined location, but do not have the size (magnitude) / dimensionless example: . P . A point A point P S1/W2/HO-1/G.11/Math/RIT-AYA/2010-2011

  3. ray AB B Line is set of the points that only have the length / one dimensionalFrom two points make a line Line example A k linek A B line segment AB S1/W2/HO-1/G.11/Math/RIT-AYA/2010-2011

  4. Y 4B 3 2 1 X -3 -2 -1 0 1 2 3 A -1 -2 Fig. 1 S1/W2/HO-1/G.11/Math/RIT-AYA/2010-2011

  5. coordinates points&lines S1/W2/HO-1/G.11/Math/RIT-AYA/2010-2011

  6. The distance between the points (x1, y1) and (x2,y2) (or the length of the line segment joining them) is The distance between two points S1/W2/HO-1/G.11/Math/RIT-AYA/2010-2011

  7. Example:1. find the length of AB BxA Fig. 2 S1/W2/HO-1/G.11/Math/RIT-AYA/2010-2011

  8. answer: S1/W2/HO-1/G.11/Math/RIT-AYA/2010-2011

  9. 2. Given A(-3,k) and B(9,-1), if the length of AB is 13 units, find possible values of k. answer: S1/W2/HO-1/G.11/Math/RIT-AYA/2010-2011

  10. 3. Given a triangle ABC, which A(-1,2), B(2,2) and C(2,6). find the length of each side of the triangle. Determine whether ∆ABC is a right-angled triangle, an isosceles triangle or neither of the above. answer: S1/W2/HO-1/G.11/Math/RIT-AYA/2010-2011

  11. The mid-point of the line segment joining(x1, y1) and (x2,y2) has coordinates The mid-point of a line segment S1/W2/HO-1/G.11/Math/RIT-AYA/2010-2011

  12. Example:1. From Fig. 2, find the mid-point of A answer: S1/W2/HO-1/G.11/Math/RIT-AYA/2010-2011

  13. 2. If M(-2,1) is the midpoint of AB, where A is (-3,2), find the coordinates of B. answer: S1/W2/HO-1/G.11/Math/RIT-AYA/2010-2011

  14. 3. A(1,5) and B(7,-9) are two points. AB divided into four equal parts at C, D and E. Find coordinates of C, D and E. answer: S1/W2/HO-1/G.11/Math/RIT-AYA/2010-2011

  15. The gradient of a line segment The gradient of the line joining (x1, y1) to (x2,y2) is S1/W2/HO-1/G.11/Math/RIT-AYA/2010-2011

  16. Example The ends of a line segment are (a-b,a+b) and (a+b,a-b). Find the length of the line segment, its gradient and the coordinates of its mid point. answer: S1/W2/HO-1/G.11/Math/RIT-AYA/2010-2011

  17. The equation of a line • The equation of the line through • (x1,y1) with gradient m is; • y–y1=m(x-x1) • The equation of the line through • A(x1,y1) and B(x2,y2) is; S1/W2/HO-1/G.11/Math/RIT-AYA/2010-2011

  18. Example1. Find the equation of the line through the point (2,-3) with gradient -1 answer: S1/W2/HO-1/G.11/Math/RIT-AYA/2010-2011

  19. 2. Find the equation of the line joining the points (3,4) and (-1,2) answer: S1/W2/HO-1/G.11/Math/RIT-AYA/2010-2011

  20. The point of intersection of two lines Suppose that you have two lines with equation 2x – y = 4 and 3x + 2y = -1. How do you find the coordinates of the point of intersection of these lines? S1/W2/HO-1/G.11/Math/RIT-AYA/2010-2011

  21. Parallel and Perpendicular Lines • Parallel lines (//) • Parallel lines have equal gradient m1=m2 • Perpendicular Lines ( ) • Two lines with gradients m1 and m2are • perpendicular if; • m1m2=-1 S1/W2/HO-1/G.11/Math/RIT-AYA/2010-2011

  22. Example1. A(2,1), B(3,4), C(-1,2) and D(-2,-1) are four points. a) which of the lines AB, BC, CD and DA are parallel? b) what type of quadrilateral is ABCD? answer: S1/W2/HO-1/G.11/Math/RIT-AYA/2010-2011

  23. 2. A line is drawn through the point (-1,2) parallel to the line y + 5x = 2. Find its equation and that of the perpendicular line through the same point answer: S1/W2/HO-1/G.11/Math/RIT-AYA/2010-2011

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