In the graph below, what is the line of reflection for triangleXYZ and triangleX'Y'Z'?
Two triangles are graphed on a coordinate grid.
Triangle X Y Z has
vertex X at left parenthesis 4 comma 5 right parenthesis.
vertex Y at left parenthesis 6 comma 3 right parenthesis.
vertex Z at left parenthesis 3 comma 2 right parenthesis.
Triangle X prime Y prime Z prime has
vertex X prime at left parenthesis 0 comma 5 right parenthesis.
vertex Y prime at left parenthesis negative 2 comma 3 right parenthesis.
vertex Z prime at left parenthesis 1 comma 2 right parenthesis.
(1 point)
Responses
the x-axis
the x -axis
the y-axis
the y -axis
x = 2
x = 2
y = 2
the y-axis
To find the line of reflection for triangle XYZ and triangle X'Y'Z', we need to determine the line that serves as the axis of reflection. This line is perpendicular to the x-axis or y-axis.
Looking at the coordinates of the vertices, we can observe that the y-coordinates change while the x-coordinates remain the same for each corresponding pair of vertices:
Triangle XYZ:
Vertex X: (4, 5)
Vertex Y: (6, 3)
Vertex Z: (3, 2)
Triangle X'Y'Z':
Vertex X': (0, 5)
Vertex Y': (-2, 3)
Vertex Z': (1, 2)
The x-coordinates for corresponding vertices do not change, but the y-coordinates change sign:
Vertex Y: (6, 3)
Vertex Y': (-2, 3)
This indicates that the line of reflection is the x-axis.
Therefore, the correct line of reflection for triangle XYZ and triangle X'Y'Z' is the x-axis.