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Mathematic

Mathematic. Straight Lines. l 1. l 2. m 2. m 1. Perpendicular with Another Lines. Slope (gradient) lines l 1 is m 1 , and the slope lines l 2 is m 2 . If l1 perpendicular with to l2 ( ) Then, m 1 .m 2 = -1…….(exam). Perpendicular with Another Lines.

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Mathematic

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  1. Mathematic Straight Lines

  2. l1 l2 m2 m1 Perpendicular with Another Lines • Slope (gradient) lines l1 is m1, and the slope lines l2 is m2. If l1 perpendicular with to l2 ( ) Then, m1.m2 = -1…….(exam)

  3. Perpendicular with Another Lines • Suppose l1 is in the form of ax + by = c then m1 = , then by (exam): or

  4. Perpendicular with Another Lines • Suppose l2 trough the point (x1,y1) then by (XI): Multiplying by a and removing bracket rearrange

  5. Substitute x=x1 y=y1 Perpendicular with Another Lines • We may write

  6. Perpendicular with Another Lines • Notice that here, c is also neglected (diabaikan). And as in the case of parallelism (formula[XII]), formula (XV) hold when the terms in x and y have been located on the same hand of equation.

  7. Perpendicular with Another Lines • If two straight lines meet at one point, then the point of intersection is located on both straight lines.

  8. Perpendicular with Another Lines • So if the lines ax + by = c and dx + ny = q meet at the point A (xA,yA) then the point A is located on the line ax + by = c, where we obtain axA + byA = c(i), and the point A is also located on the line dx + ny = q, where we obtain dxA + nyA = q(ii).

  9. Perpendicular with Another Lines • Multiplying by n in (i) and multiplying by b in (ii), then subtract.

  10. Perpendicular with Another Lines • While multiplying by d in (i) and multiplying by a in (ii), then subtract

  11. Perpendicular with Another Lines • Which means, if the line ax + by = c intersects the line dx + ny = q then the point of is the point • If abscise of point of intersection has been obtained, then its coordinate can be obtained by substituting that abscise into one equation of concurrent straight lines.

  12. Creates by • Abid Famasya • Siswanto Adi W • Pugar Arga • Safira Rahmaningrum • Nurlaili A Risfa

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