In ∆ABC, D and E are the midpoint of the sides BC and AC
respectively. Find the length of DE. Prove that DE = 1 AB 2
A=(-6,-1)B=(2,-2)C=(4,-2)
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In triangle ABC, point D is the midpoint of AC and point E is the midpoint of BC. How do you use vectors to prove that DE = 1/2AB?
We define 2 vectors: u⃗ =B−A,v⃗ =C−Au→=B−A,v→=C−A.
We assign point A to be the origin. Then, points E and D can be given as follows.E=u⃗ +12(v⃗ −u⃗ )=12u⃗ +12v⃗ D=12v⃗ E=u→+12(v→−u→)=12u→+12v→D=12v→
Finally,⇒DE=∥E−D∥=∥∥(12u⃗ +12v⃗ )−(12v⃗ )∥∥=12∥u⃗ ∥=12∥B−A∥=12ABDE=12AB.In triangle ABC, point D is the midpoint of AC and point E is the midpoint of BC. How do you use vectors to prove that DE = 1/2AB?
We define 2 vectors: u⃗ =B−A,v⃗ =C−Au→=B−A,v→=C−A.
We assign point A to be the origin. Then, points E and D can be given as follows.E=u⃗ +12(v⃗ −u⃗ )=12u⃗ +12v⃗ D=12v⃗ E=u→+12(v→−u→)=12u→+12v→D=12v→
Finally,⇒DE=∥E−D∥=∥∥(12u⃗ +12v⃗ )−(12v⃗ )∥∥=12∥u⃗ ∥=12∥B−A∥=12ABDE=12AB.
Hope This Helps :)
We define 2 vectors: u⃗ =B−A,v⃗ =C−Au→=B−A,v→=C−A.
We assign point A to be the origin. Then, points E and D can be given as follows.E=u⃗ +12(v⃗ −u⃗ )=12u⃗ +12v⃗ D=12v⃗ E=u→+12(v→−u→)=12u→+12v→D=12v→
Finally,⇒DE=∥E−D∥=∥∥(12u⃗ +12v⃗ )−(12v⃗ )∥∥=12∥u⃗ ∥=12∥B−A∥=12ABDE=12AB.In triangle ABC, point D is the midpoint of AC and point E is the midpoint of BC. How do you use vectors to prove that DE = 1/2AB?
We define 2 vectors: u⃗ =B−A,v⃗ =C−Au→=B−A,v→=C−A.
We assign point A to be the origin. Then, points E and D can be given as follows.E=u⃗ +12(v⃗ −u⃗ )=12u⃗ +12v⃗ D=12v⃗ E=u→+12(v→−u→)=12u→+12v→D=12v→
Finally,⇒DE=∥E−D∥=∥∥(12u⃗ +12v⃗ )−(12v⃗ )∥∥=12∥u⃗ ∥=12∥B−A∥=12ABDE=12AB.
Hope This Helps :)
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