A triangle has corners at #(4, 6 )#, ( 1 , -3)#, and #( 1 , -4)#. What will the new coordinates of the triangle be if it is reflected across the x-axis?
(4,-6), (1,3), and (1,4).
When reflected across the x-axis, each of the y-coordinates changes sign. That is, a point (a,b) means it is at x=a and y=b, since the reflection is made across the x-axis, the x-coordinate stays the same. However, y=b means the point is b units away from the x-axis, so with reflection it is again b units away from the x-axis, but on the other side, so the sign changes.