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In the figure, C and D are mid points of OA and AB respectively. OD and BC intersect at E. OE : ED =r :1 and BE : EC =m :1. (a) Find the coordinates of C and D. (b) Prove that the coordinates of E A (2a, 26) 4ra rb `1+r' 1+r' are (c) Prove that the coordinates of E в (ба, 0) (6+ m)а тb are OE: ED =r: 1; 1+m 1+m BE: EC = m: 1 (d) Hence find the values of r and m.

In the figure, C and D are mid points of OA and AB respectively. OD and BC intersect at E. OE : ED =r :1 and BE : EC =m :1. (a) Find the coordinates of C and D. (b) Prove that the coordinates of E A (2a, 26) 4ra rb `1+r' 1+r' are (c) Prove that the coordinates of E в (ба, 0) (6+ m)а тb are OE: ED =r: 1; 1+m 1+m BE: EC = m: 1 (d) Hence find the values of r and m.

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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3 HK VOLTE ull a 16% D 23:02 Homework 13... Homework (13) 5. In the figure, E divides line segments AB and CD into two parts in the ratio of 2:3 А(3, 2) respectively. (a) Find the coordinates of E. (b) Find the coordinates of D. C(5, -4) (c) Are AC and DB parallel to each other? B(-2, -8) Explain briefly for your answer. 6. In the figure, Cand D are mid points of OA and AB respectively. OD and BC intersect at E. OE : ED =r:1 and BE : EC = m: 1. (a) Find the coordinates of C and D. (b) Prove that the coordinates of E A (2a, 2b) 4ra rb are 1+r 1+r (c) Prove that the coordinates of E в (ба, 0) mb -). 1+ m (6+m)a are ( OE : ED =r: 1; BE: EC = m: 1 1+m (d) Hence find the values of r and m.
Transcribed Image Text:3 HK VOLTE ull a 16% D 23:02 Homework 13... Homework (13) 5. In the figure, E divides line segments AB and CD into two parts in the ratio of 2:3 А(3, 2) respectively. (a) Find the coordinates of E. (b) Find the coordinates of D. C(5, -4) (c) Are AC and DB parallel to each other? B(-2, -8) Explain briefly for your answer. 6. In the figure, Cand D are mid points of OA and AB respectively. OD and BC intersect at E. OE : ED =r:1 and BE : EC = m: 1. (a) Find the coordinates of C and D. (b) Prove that the coordinates of E A (2a, 2b) 4ra rb are 1+r 1+r (c) Prove that the coordinates of E в (ба, 0) mb -). 1+ m (6+m)a are ( OE : ED =r: 1; BE: EC = m: 1 1+m (d) Hence find the values of r and m.
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