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.

A (1,-4) B (3, 2) C (4,-2)

ok thnx :)

no problem!!

To find the coordinates of the image A'B'C' after a reflection over the x-axis, you need to use the following rule:

For a point (x, y) reflected over the x-axis, the coordinates of its image will be (x, -y).

Let's apply this rule to each of the points A(1,4); B(3,-2); and C(4,2):

For point A(1,4), the x-coordinate remains the same, and the y-coordinate changes sign:
The image of A(1,4) is A'(1,-4).

For point B(3,-2), the x-coordinate remains the same, and the y-coordinate changes sign:
The image of B(3,-2) is B'(3,2).

For point C(4,2), the x-coordinate remains the same, and the y-coordinate changes sign:
The image of C(4,2) is C'(4,-2).

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