Question

The transformation (x,y) (x+4,y-3 is performed on the segment AB.The imgae is the line segment A’B’ where point A’=(3,-3) and point B’ =(5,-3).What are the coordinates of A and B in the line segment AB

Answer 1

Answer:

$A= (-1,0)\\B=(1,0)$

Step-by-step explanation:

The transformation of the segment AB is:

$(x+4,\ y-3)$

Given the points of the line segment A'B':

$A'=(3,-3)$ and  $B'=(5,-3)$

The coordinates of the points A and B in the line segment AB,can be calculated through this procedure:

For A:

x-coordinate:

Substitute the x-coordinate of A' (we can represent it with$x_{(A')}$) into $x_{(A')}=x_A+4$ and solve for $x_{A}$, which is the x-coordinate of A:

$x_{(A')}=x_A+4\\\\3=x_A+4\\\\3-4=x_A\\\\x_A=-1$

y-coordinate:

Substitute the y-coordinate of A' (we can represent it with$y_{(A')}$) into $y_{(A')}=y_A-3$ and solve for $y_{A}$, which is the y-coordinate of A:

$y_{(A')}=y_A-3\\\\-3=y_A-3\\\\-3+3=y_A\\\\y_A=0$

The point of A is: (-1,0)

For B:

x-coordinate:

Substitute the x-coordinate of B' (we can represent it with$x_{(B')}$) into $x_{(B')}=x_B+4$ and solve for $x_{B}$, which is the x-coordinate of B:

$x_{(B')}=x_B+4\\\\5=x_B+4\\\\5-4=x_B\\\\x_B=1$

y-coordinate:

Substitute the y-coordinate of B' (we can represent it with$y_{(B')}$) into $y_{(B')}=y_B-3$ and solve for $y_{B}$, which is the y-coordinate of B:

$y_{(B')}=y_B-3\\\\-3=y_B-3\\\\-3+3=y_B\\\\y_B=0$

The point of B is: (1,0)