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
for a reflection over the x-axis, the x's stay the same, but the y's change to their opposites.
I will do point B
B(3,-2) ----> B' (3,2)
you do the rest.
I suggest to make a sketch to confirm what you did
a triangle has coordinates A(1,2),B(4,-2), and C(1,1) graph the triangle.
To find the coordinates of the image A'B'C' after a reflection over the x-axis, we need to reflect each point over the x-axis.
For point A(1, 4), the image A' will have the same x-coordinate but the y-coordinate will be negated. So the coordinates of A' will be (1, -4).
For point B(3, -2), the image B' will have the same x-coordinate but the y-coordinate will be negated. So the coordinates of B' will be (3, 2).
For point C(4, 2), the image C' will have the same x-coordinate but the y-coordinate will be negated. So the coordinates of C' will be (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)
C' (4, -2)
To find the image A'B'C' after reflecting the triangle ABC over the x-axis, we need to invert the y-coordinates of each vertex.
The reflection over the x-axis takes a point (x, y) to the point (x, -y). So, for each vertex, we will keep the x-coordinate the same, but negate the y-coordinate.
Let's apply this to each vertex:
Vertex A: (1, 4)
The x-coordinate remains the same: 1
The y-coordinate becomes its negation: -4
Therefore, the coordinates of A' are (1, -4).
Vertex B: (3, -2)
The x-coordinate remains the same: 3
The y-coordinate becomes its negation: -(-2) = 2
Therefore, the coordinates of B' are (3, 2).
Vertex C: (4, 2)
The x-coordinate remains the same: 4
The y-coordinate becomes its negation: -2
Therefore, the coordinates of C' are (4, -2).
So, the coordinates of the image triangle A'B'C' after a reflection over the x-axis are:
A' (1, -4),
B' (3, 2),
C' (4, -2).