Question

If BA [a= (-2,-3) b= (1,2)] is extended all the way through A creating a BF and A becomes the midpoint of BF, then what are the coordinates

Answer 1

Answer:

(-5,-8)

Step-by-step explanation:

If M(x,y) is the midpoint of the segment CD, where $C(x_1,y_1),\ D(x_2,y_2),$ then

$x=\dfrac{x_1+x_2}{2}\\ \\y=\dfrac{y_1+y_2}{2}$

You are given two points A(-2,-3) and B(1,2), let point F be the point with coordinates (x,y). Yuo know, that point A is the midpoint of BF, then

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

Substitute known coordinates:

$-2=\dfrac{1+x}{2}\Rightarrow 1+x=-4,\ \ x=-5\\ \\-3=\dfrac{2+y}{2}\Rightarrow 2+y=-6,\ \ y=-8$

So, point F has coordinates (-5,-8)