Question

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

Answer 1

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,

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