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.
(Show your work)
reflection in the x-axis just takes
(x,y) -> (x,-y)
so, just change the sign of all the y-coordinates.
Steve, is it??
A(1,4) -> A'(1,-4)
B(3,-2) -> B'(3,2)
C(4,1) -> C'(4,-2)
To find the coordinates of the image A'B'C' after a reflection over the X-axis, we need to reflect each individual point over the X-axis.
Let's begin with point A(1,4). When we reflect a point over the X-axis, the y-coordinate becomes its opposite value.
So when we reflect point A(1,4) over the X-axis, the new coordinates will be:
A'(1, -4).
Next, let's consider point B(3,2). Similarly, when we reflect point B over the X-axis, the y-coordinate becomes its opposite value.
So when we reflect point B(3,2) over the X-axis, the new coordinates will be:
B'(3, -2).
Lastly, let's look at point C(4,2). Again, when we reflect point C over the X-axis, the y-coordinate becomes its opposite value.
So when we reflect point C(4,2) over the X-axis, the new coordinates will be:
C'(4, -2).
Therefore, 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).
To find the coordinates of the image A'B'C' after a reflection over the X-axis, we need to find the new y-coordinates of each point while keeping the x-coordinates the same.
Vertices of triangle ABC:
A(1, 4)
B(3, 2)
C(4, 2)
To reflect a point (x, y) over the X-axis, you change the sign of the y-coordinate, while keeping the x-coordinate the same.
For point A(1, 4), the image A' will have the same x-coordinate, but the y-coordinate will be the negative of the original y-coordinate.
So, A'(1, -4)
For point B(3, 2), the image B' will have the same x-coordinate, but the y-coordinate will be the negative of the original y-coordinate.
So, B'(3, -2)
For point C(4, 2), the image C' will have the same x-coordinate, but the y-coordinate will be the negative of the original y-coordinate.
So, C'(4, -2)
Therefore, the coordinates of the image triangle A'B'C' after reflection over the X-axis are:
A'(1, -4)
B'(3, -2)
C'(4, -2)