Find vector D

Question

I hva 3 points A(-1 , 6) B(2 , 1) and C(4 , 4)

 

Then I have to find D, given that vector AB+CD=0 (origo) 

 

I tried to find AB(3 , 5) and AC(2 , 5) first. 

 

But I am struggling with D. Are there any steps or methods I could use to find it out?

Answer 1

Let D have coordinates (x,y).

 

You want AB + CD = 0

 

AB = [(2 - (-1)]i + (1 - 6)j = 3i - 5j

 

CD = (x - 4)i + (y - 4)j

 

AB + CD = (3 + x - 4)i + (-5 + y - 4)j = (x - 1)i + (y - 9)j = 0i + 0j ⇒

 

x - 1 = 0

y - 9 = 0

 

x = 1

y = 9

 

Test the answer.