Triangle ABC has coordinates A(1, 4); B(3, –2); and C(4, 2). Find the coordinates of the image A'B'C' after a reflection over the x-axis.
reflection in the x-axis takes (x,y) --> (x,-y)
so, just change the sign of the y-coordinate of each point.
e.g. (4,3) --> (4,-3)
(4,3) is the answer?
No. The answer is you change the y-coordinate signs of the points you were given! e.g. means "for example".
To find the coordinates of the image A'B'C' after a reflection over the x-axis, we need to flip the y-coordinates of each point.
Given that the coordinates of A are (1, 4), the x-coordinate remains the same, but the y-coordinate becomes its negation:
A' = (1, -4)
Similarly, for point B with coordinates (3, -2), the x-coordinate remains the same, but the y-coordinate becomes its negation:
B' = (3, 2)
For point C with coordinates (4, 2), the x-coordinate remains the same, but the y-coordinate becomes its negation:
C' = (4, -2)
So, the coordinates of the image A'B'C' after a reflection over the x-axis are A'(1, -4), B'(3, 2), and C'(4, -2).