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# Matematika - Projection Of Lne To Plane

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• 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. Solution H G The distance of line:E a. AB to line HG F = AH (AH &#xF05E; AB, AH &#xF05E; HG) D C = 4&#x221A;2 (side diagonal)A 4 cm B b.AD to line HF = DH (DH &#xF05E; AD, DH &#xF05E; HF = 4 cm 2
• 3. H Q G The distance of line:E F b.BD to line EG = PQ (PQ &#xF05E; BD, D C PQ &#xF05E; EGA P = AE 4 cm B = 4 cm 3
• 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&#x2019; g&#x2019; B&#x2019;So, the projection of line g to the planeH is g&#x2019; 4
• 5. Example 1 H GE Given cube F ABCD.EFGH a. The projection of line D EF to plane ABCD C is&#x2026;.A B b. If the length of edge is 6 cm, The length of projection line CG to plane BDG is &#x2026;. 5
• 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. 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. H G &#x2022;The length of PG is:E F &#x2022;PG = &#x2154;.GR P = &#x2154;.&#xBD;a&#x221A;6 D CA R B = &#x2153;a&#x221A;6 = &#x2153;.6&#x221A;6 6 cm&#x2022;So, the length of projection fromline CG to plane BDG is 2&#x221A;6 cm 8
• 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 &#x2026;.A 16 cm B 9
• 10. Solution Projection of TA to T plane ABCD is AT&#x2019;. Length of AT&#x2019;= &#xBD;AC = &#xBD;.16&#x221A;2 D C = 8&#x221A;2 T&#x2019;A 16 cm B So, the length of projection from line TA to plane ABCD is 8&#x221A;2 cm 10
• 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 &#x2026;