triangle abc has coordinates a(1 4) b( 3, -2); and c( 4, 2) find the coordinates of the image ABC after a reflection over the x- axis

reflection over the x-axis takes (x,y) -> (x,-y)

So, just change the sign of all the y-coordinates in your points.

To find the coordinates of the image ABC after a reflection over the x-axis, we need to change the sign of the y-coordinate of each point.

Let's take each point one by one and apply the reflection:

For point A(1, 4), the reflection changes the sign of the y-coordinate. So, the new coordinates of A' will be (1, -4).

For point B(3, -2), the reflection changes the sign of the y-coordinate. So, the new coordinates of B' will be (3, 2).

For point C(4, 2), the reflection changes the sign of the y-coordinate. So, the new coordinates of C' will be (4, -2).

Therefore, the coordinates of the image ABC after a reflection over the x-axis are A'(1, -4), B'(3, 2), and C'(4, -2).