Find the coordinates of the image of the point 1 2 , 3 4 under the reflection in the line y = 0 .

Given point is 1 2 , 3 4 . We have to find the coordinates of the image of this point under the reflection in X - axis. Let A x , y be any point in the coordinate plane, then A ' x , - y is the reflection in the X - axis, i.e., y = 0 . Example, for the point 1 , 2 , its reflection in the X - axis is 1 , - 2 Here, the given point is P 1 2 , 3 4 , then its reflection in the X - axis is P ' 1 2 , - 3 4 . Hence, the reflection of the point 1 2 , 3 4 in the X - axis, is the point 1 2 , - 3 4 .

Find the coordinates of the image of the point 3 2 , 5 2 under the reflection in the line x = 0 .

Given: Line x = 0 and point 3 2 , 5 2 We have to find the image of the point 3 2 , 5 2 under the reflection in the line x = 0 . We know that, the image of a point P x , y under the reflection in the line x = a is P ' - x + 2 a , y . The given line is x = 0 , then the image of a point P ( x , y ) under the reflection will be P ' - x , y , i.e. only the sign of x - coordinate will be changed. Hence, the image of point P 3 2 , 5 2 under the reflection in the line x = 0 is P ' - 3 2 , 5 2 .