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

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

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)