Use the image to answer the question.
Triangle upper X upper Y upper Z and a dotted line are graphed on a coordinate plane. The x- and y-axes range from negative 7 to 7 in increments of 1. The dotted line is labeled axis of reflection and follows y equals 1.
Find the coordinates of Z′ after a reflection across y=1.
(1 point)
Responses
Z′(−4,2)
upper Z prime left parenthesis negative 4 comma 2 right parenthesis
Z′(4,0)
upper Z prime left parenthesis 4 comma 0 right parenthesis
Z′(6,2)
upper Z prime left parenthesis 6 comma 2 right parenthesis
Z′(−4,0)
Based on the image, the coordinates of Z are (4, 2). Since we are reflecting across the line y = 1, the y-coordinate remains the same while the x-coordinate becomes its opposite.
Therefore, Z′ has the coordinates (-4, 2).
To find the coordinates of Z' after a reflection across y=1, we need to locate the point Z on the coordinate plane and determine its reflection.
Based on the information provided, Z is the vertex of the triangle. The dotted line labeled "axis of reflection" follows y=1.
By considering the distance between Z and the reflection line, we can determine the new coordinates of Z'.
Looking at the options given, Z'(-4,2) has a reflection line distance of -1 (y-coordinate decreases by 1).
Therefore, the correct answer is Z'(-4,0).