The coordinates of the vertices of triangleCDE are C(1, 4), D(3, 6), and E(7, 4). If the triangle is reflected over the line y = 3, what are the coordinates of the image of D?
(1 point)
Responses
(3, –6)
(3, –6)
(3, –3)
(3, –3)
(3, 0)
(3, 0)
(3, 9)
To reflect a point over the line y = 3, we need to find the new y-coordinate by subtracting the difference between the original y-coordinate and the line of reflection from the line of reflection.
The line of reflection is y = 3. The original y-coordinate of D is 6. The difference between the original y-coordinate and the line of reflection is 6-3 = 3.
The new y-coordinate of the image of D is 3 - 3 = 0.
The x-coordinate remains the same.
Therefore, the coordinates of the image of D are (3, 0).
The correct answer is (3, 0).
To reflect a point over the line y = 3, we need to find the distance between the point and the line, and then shift the point the same distance but in the opposite direction.
The distance between the line y = 3 and the point D(3, 6) is 6 - 3 = 3.
To find the image of D, we need to shift it 3 units below the line.
Therefore, the coordinates of the image of D are (3, 6 - 3) = (3, 3).
So the correct answer is (3, -3).