Matematika - Projection Of Lne To Plane

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Matematika - Projection Of Lne To Plane

  1. 1. H G Given cubeE F ABCD.EFGH with the length of edge is 4 cm. Determine the distance of : D CA 4 cm B a.Line AB to line HG b.Line AD to line HF c.Line BD to line EG 1
  2. 2. Solution H G The distance of line:E a. AB to line HG F = AH (AH  AB, AH  HG) D C = 4√2 (side diagonal)A 4 cm B b.AD to line HF = DH (DH  AD, DH  HF = 4 cm 2
  3. 3. H Q G The distance of line:E F b.BD to line EG = PQ (PQ  BD, D C PQ  EGA P = AE 4 cm B = 4 cm 3
  4. 4. Projection of line to plane We can make the A projection of line to plane B by projection some g points in the line to plane. A’ g’ B’So, the projection of line g to the planeH is g’ 4
  5. 5. Example 1 H GE Given cube F ABCD.EFGH a. The projection of line D EF to plane ABCD C is….A B b. If the length of edge is 6 cm, The length of projection line CG to plane BDG is …. 5
  6. 6. Solution : H GE a. The projection of line F EF to the plane ABCD is determining the projection of point D C E and F to the planeA B ABCD, they are point A and B.So, the projection of line EF to theplane ABCD is line AB. 6
  7. 7. b. The projection of line H G CG to plane BDG isE F determining the projection of point C P and G to plane BDG, D they are point P and C G.A 6 cm BSo, the projection of line CG toplane BDG is line PG. 7
  8. 8. H G •The length of PG is:E F •PG = ⅔.GR P = ⅔.½a√6 D CA R B = ⅓a√6 = ⅓.6√6 6 cm•So, the length of projection fromline CG to plane BDG is 2√6 cm 8
  9. 9. Example 2 Given regular pyramid T T.ABCD with the length of AB= 16 cm, TA = 18 cm. The length of projection D C TA to plane ABCD is ….A 16 cm B 9
  10. 10. Solution Projection of TA to T plane ABCD is AT’. Length of AT’= ½AC = ½.16√2 D C = 8√2 T’A 16 cm B So, the length of projection from line TA to plane ABCD is 8√2 cm 10
  11. 11. Activities class1. Given the cube ABCD.EFGH with the length of edge is 6 cm. Determine the length of projection from line AG to : a.Plane ABCD b.Plane ADHE c.If M is the cut point from side diagonals in plane ABCD. The length of projection from line GM to plane BCGF is …

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