Triangle ABC has coordinates A(1,4) B (3, -2)C ( 4, 2). Find the coordinates of the image ABC prime after a reflection over the X - axis.
each point (x,y) -> (x,-y)
just swap the sign of the y-coordinate for each point.
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 while keeping the x-coordinate the same.
Given triangle ABC with coordinates A(1,4), B(3,-2), and C(4,2), let's find the coordinates of each point after the reflection.
1. For point A(1,4):
- The x-coordinate remains the same: x = 1
- To reflect over the x-axis, change the sign of the y-coordinate: y' = -4
Therefore, A' is located at (1, -4).
2. For point B(3,-2):
- The x-coordinate remains the same: x = 3
- To reflect over the x-axis, change the sign of the y-coordinate: y' = 2
Therefore, B' is located at (3, 2).
3. For point C(4,2):
- The x-coordinate remains the same: x = 4
- To reflect over the x-axis, change the sign of the y-coordinate: y' = -2
Therefore, C' is located at (4, -2).
So, the coordinates of the image ABC' after reflection over the x-axis are A'(1, -4), B'(3, 2), and C'(4, -2).
To find the coordinates of the image ABC' after a reflection over the X-axis, we need to flip the triangle over the X-axis.
The X-axis is a horizontal line that goes through the point (0,0).
To reflect a point over the X-axis, we keep the X-coordinate the same and change the sign of the Y-coordinate.
Let's go through each point of the triangle and find their reflections.
Point A(1, 4):
To reflect A over the X-axis, we keep the X-coordinate (1) the same and change the sign of the Y-coordinate (4). So, the reflected point is A'(1, -4).
Point B(3, -2):
To reflect B over the X-axis, we keep the X-coordinate (3) the same and change the sign of the Y-coordinate (-2). So, the reflected point is B'(3, 2).
Point C(4, 2):
To reflect C over the X-axis, we keep the X-coordinate (4) the same and change the sign of the Y-coordinate (2). So, the reflected point is C'(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).