Question

A line segment has endpoints at (3, 2) and (2, –3). Which reflection will produce an image with endpoints at (3, –2) and (2, 3)? A.a reflection of the line segment across the x-axis B. a reflection of the line segment across the y-axis C. a reflection of the line segment across the line y = x D.a reflection of the line segment across the line y = –x

Answer 1

For this case we have the following points:

(3, 2)

(2. 3)

We apply the following transformation:

(x, y) -------------> (x, -y) ----------------> (x ', y')

This transformation represents a reflection of the points on the x axis.

We have then:

(3, 2) -------------> (3, - (2)) ----------------> (3, -2)

(2, -3) -------------> (2, - (- 3)) ----------------> (2, 3 )

We observe that the points obtained are the points that are sought.

Answer:

A. a reflection of the line segment across the x-axis

Answer 2

         We have to find which reflection will produce an image, if the endpoints of the line segment are ( 3, 2 ) and ( 2, - 3 ) and the endpoints of an image are ( 3, - 2 ) and ( 2 , 3 ). We can see that the first coordinate ( x - coordinate ) stays the same and the y - coordinates change their sign. 
         Answer:
         A ) A reflection of the line segment across the x - axis.