In the graph below, what is the line of reflection for XYZ and X'Y'Z'? 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 line of reflection for XYZ and X'Y'Z' is the y-axis.
To find the line of reflection for Triangle XYZ and Triangle X'Y'Z', we need to determine the axis of reflection.
Step 1: Calculate the midpoints of corresponding sides of Triangle XYZ and Triangle X'Y'Z':
- The midpoint of XY is ((4+6)/2, (5+3)/2) = (5, 4).
- The midpoint of X'Y' is ((0+(-2))/2, (5+3)/2) = (-1, 4).
Step 2: Draw a line connecting these midpoints:
- The line connecting (5, 4) and (-1, 4) is a horizontal line on the y-axis.
Step 3: Determine the axis of reflection:
- The line connecting the midpoints is parallel to the x-axis.
- Therefore, the axis of reflection is the x-axis.
So, the line of reflection for Triangle XYZ and Triangle X'Y'Z' is the x-axis.
To determine the line of reflection for triangle XYZ and X'Y'Z', we can visually analyze the transformation between the original triangle and its reflected image.
The line of reflection is the line that divides the plane into two equal halves, such that each point on one side is equidistant from the corresponding point on the other side.
Given the coordinates of the vertices, we can compare the x-coordinates and y-coordinates of the corresponding points to identify the line of reflection.
Considering the x-coordinates, we notice that the x-coordinate of point X' (-2) is obtained by subtracting the x-coordinate of point X (4) from 0 (the x-coordinate of the line of reflection). Similarly, the x-coordinate of point Y' (0) is obtained by subtracting the x-coordinate of point Y (6) from 0, and the x-coordinate of point Z' (-1) is obtained by subtracting the x-coordinate of point Z (3) from 0.
Therefore, we can conclude that the line of reflection is the y-axis (vertical line passing through x = 0), as all the x-coordinates are negated versions of the original x-coordinates.
Hence, the correct answer is: the y-axis.