triangle ABC with vertices A(-2 1) and C(-4 3), B(-4 1) is reflected on the x axis to give it's image triangle A'B'C is then reflected in the Y axis to give a second triangle image A"B"C
just flip the signs of all the coordinates
first y, then x
To find the image of triangle ABC after reflecting it over the x-axis, we need to change the y-coordinates of each vertex to their opposite value.
Given that the vertices of triangle ABC are A(-2, 1), B(-4, 1), and C(-4, 3), we can perform the reflection as follows:
1. Reflect point A(-2, 1) over the x-axis:
The x-coordinate remains the same, but the y-coordinate changes to its opposite, so A' is (A' -2, -1).
2. Reflect point B(-4, 1) over the x-axis:
The x-coordinate remains the same, but the y-coordinate changes to its opposite, so B' is (B' -4, -1).
3. Reflect point C(-4, 3) over the x-axis:
The x-coordinate remains the same, but the y-coordinate changes to its opposite, so C' is (C' -4, -3).
Hence, the image triangle after reflecting triangle ABC over the x-axis is A'B'C' with vertices A'(-2, -1), B'(-4, -1), and C'(-4, -3).
To find the image of triangle A'B'C' after reflecting it over the y-axis, we need to change the x-coordinates of each vertex to their opposite value.
Given the vertices of triangle A'B'C' as A'(-2, -1), B'(-4, -1), and C'(-4, -3), we can perform the reflection as follows:
1. Reflect point A'(-2, -1) over the y-axis:
The y-coordinate remains the same, but the x-coordinate changes to its opposite, so A" is (-A", -1).
2. Reflect point B'(-4, -1) over the y-axis:
The y-coordinate remains the same, but the x-coordinate changes to its opposite, so B" is (-B", -1).
3. Reflect point C'(-4, -3) over the y-axis:
The y-coordinate remains the same, but the x-coordinate changes to its opposite, so C" is (-C", -3).
Hence, the second image triangle after reflecting triangle A'B'C' over the y-axis is A"B"C" with vertices A"(-(-2), -1), B"(-(-4), -1), and C"(-(-4), -3), which simplifies to A"(2, -1), B"(4, -1), and C"(4, -3).
To find the coordinates of the image triangle A'B'C' after reflecting triangle ABC across the x-axis, you need to:
1. Flip the sign of the y-coordinate of each vertex.
Given triangle ABC with vertices A(-2, 1), B(-4, 1), and C(-4, 3), the image triangle A'B'C' after reflecting across the x-axis will have the following coordinates:
A'(-2, -1)
B'(-4, -1)
C'(-4, -3)
Next, to find the coordinates of the second image triangle A"B"C" after reflecting triangle A'B'C' across the y-axis, you need to:
1. Flip the sign of the x-coordinate of each vertex.
Using the coordinates of triangle A'B'C', the second image triangle A"B"C" will have the following coordinates:
A"(-(-2), -1) => A"(2, -1)
B"(-(-4), -1) => B"(4, -1)
C"(-(-4), -3) => C"(4, -3)
Hence, the coordinates of the second image triangle A"B"C" after reflecting triangle A'B'C' across the y-axis are A"(2, -1), B"(4, -1), and C"(4, -3).