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vector AB has an initial point (4,3) and terminal point (-5,1). Determine the coordinates of the terminal point of AC if AC = -2AB

A. (-9,-2)
B. (18,4)
C. (22,7)
D. (-4,-3)

Respuesta :

(22,7) I Took the quiz and that the answer

Let's assume

point C=(x,y)

we are given

A=(4,3)

B=(-5,1)

now, we can find vector AB

[tex] AB=(-5,1)-(4,3) [/tex]

[tex] AB=(-9,-2) [/tex]

now, we can find AC

[tex] AC=(x,y)-(4,3) [/tex]

[tex] AC=((x-4) , (y-3)) [/tex]

now, we are given

[tex] AC=-2AB [/tex]

now, we can plug values

and we get

[tex] ((x-4) , (y-3))=-2(-9,-2) [/tex]

[tex] ((x-4) , (y-3))=(18,4) [/tex]

now, we can equate them equal

and then we can solve for x and y

[tex] x-4=18 [/tex]

[tex] x=22 [/tex]

[tex] y-3=4 [/tex]

[tex] y=7 [/tex]

so, point C is (22,7).........Answer

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