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sdas [7]
2 years ago
9

if BA is extended all the way through A creating BF and A becomes the midpoint of BF, then what are the coordinates of F

Mathematics
1 answer:
gogolik [260]2 years ago
3 0

Answer:

F(2x_A-x_B,2y_A-y_B)

Step-by-step explanation:

Let points A, B and F have coordinates A(x_A,y_A),  B(x_B,y_B) and F(x_F,y_F).

If BA is extended all the way through A creating BF and A becomes the midpoint of BF, then the midpoint A of the segment BF has coordinates:

\dfrac{x_B+x_F}{2}=x_A\\ \\\dfrac{y_B+y_F}{2}=y_A

Express coordinates of point F:

x_B+x_F=2x_A\Rightarrow x_F=2x_A-x_B\\ \\y_B+y_F=2y_A\Rightarrow y_F=2y_A-y_B

Hence,

F(2x_A-x_B,2y_A-y_B)

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