Question

0 A C D a E b In the diagram, OAB and OED are straight lines. O is the origin, A is the midpoint of OB and E is the midpoint of AC. AC = a and CB = b. Find, in terms of a and b, in its simplest form (i) \overrightarrow{AB}, (ii) \overrightarrow{OE}, \overrightarrow{AB} = \overrightarrow{OE} = (iii) the position vector of D. B NOT TO SCALE

          0
A
C
D
a
E
b
In the diagram, OAB and OED are straight lines.
O is the origin, A is the midpoint of OB and E is the midpoint of AC.
AC = a and CB = b.
Find, in terms of a and b, in its simplest form
(i) \overrightarrow{AB},
(ii) \overrightarrow{OE},
\overrightarrow{AB} = 
\overrightarrow{OE} = 
(iii) the position vector of D.
B
NOT TO
SCALE

0
A
C
D
a
E
b
In the diagram, OAB and OED are straight lines.
O is the origin, A is the midpoint of OB and E is the midpoint of AC.
AC = a and CB = b.
Find, in terms of a and b, in its simplest form
(i) AB,
(ii) OE,
AB =
OE =
(iii) the position vector of D.
B
NOT TO
SCALE

Added by Haley M.

Geometry A Common Core Curriculum

Ron Larson, Laurie Boswell 1st Edition

Instant Answer

Solved by Expert Nick Johnson

Step 1

This means that OB is twice the length of OA. Since OA is equal to AB, we can say that AB = 2OA. Therefore, AB = 2a. (ii) To find OE, we can use the fact that E is the midpoint of AC. This means that AC is twice the length of AE. Since AE is equal to OE, we can Show more…

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Help with the part (iii) in particular. Clear explanations would be preferable. NOT TO SCALE In the diagram OAB and OED are straight lines. Q is the origin. O is the midpoint of OB and E is the midpoint of AC. AC and CB = b. Find, in terms of a and b, in its simplest form: (i) AB (ii) OE (iii) the position vector of D.