Triangle XYZ has vertices X(- 1, 1), Y(- 3, 1), and Z( -2, 5). Reflect triangle XYZ in the y-axis. Find the vertices of the image
Reflection about the y-axis has the transformation defined as:
T(x,y)→(-x,y).
For example, the point (5,4) reflected about the y-axis becomes (-5,4), according to the rule.
Apply the rule to all three vertices (in the same order) of the given triangle to get the image.
To reflect a point in the y-axis (also known as the vertical axis), we need to change the sign of its x-coordinate while keeping the y-coordinate the same.
Let's apply this rule to each vertex of the triangle XYZ.
Vertex X(-1, 1):
Since we need to change the sign of the x-coordinate, reflecting this point in the y-axis will give us the point X'(1, 1).
Vertex Y(-3, 1):
Applying the same rule, reflecting Y in the y-axis gives us Y'(3, 1).
Vertex Z(-2, 5):
Reflecting Z in the y-axis will give us Z'(2, 5), as we change the sign of the x-coordinate while keeping the y-coordinate the same.
So, the vertices of the image triangle after reflecting triangle XYZ in the y-axis are:
X'(1, 1)
Y'(3, 1)
Z'(2, 5)