Question

PLEASE HELP!!!

the transformation (x,y) to (x+4, y-3) is performed on the line segment AB. The image 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 line segment AB?

Answer 1

A'=(3,-3)

A=(3-4,-3+3)

A=(-1,0)

B'=(5,-3)

B=(5-4,-3+3)

B=(1,0)

Answer 2

Answer: The co-ordinates of the points A and B are (-1, 0) and (1, 0) respectively.

Step-by-step explanation: Given that the following transformation is applied on the line segment AB and the image is a line segment A'B', where point A'= (3,-3) and point B' = (5,-3).

(x, y) ⇒ (x+4, y-3).

We are to find the coordinates of A and B in line segment AB.

Let, the co-ordinates of points A and B be (a, b) and (c, d) respectively.

So, we have

(a, b) ⇒ (a+4, b-3) = (3, -3),

(c, d) ⇒ (c+4, d-3) = (5, -3).

This implies that

`a+4=3~~~\Rightarrow a=3-4~~~\Rightarrow a=-1,\\\\b-3=-3~~~\Rightarrow b=-3+3~~~\Rightarrow b=0,\\\\c+4=5~~~\Rightarrow c=5-4~~~\Rightarrow c=1,\\\\d-3=-3~~~\Rightarrow d=-3+3~~~\Rightarrow d=0.`

Thus, the co-ordinates of the points A and B are (-1, 0) and (1, 0) respectively.