The coordinates of the vertices of CDE 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 keep the x-coordinate the same and change the sign of the y-coordinate.
The coordinates of point D are (3, 6).
If we reflect point D over the line y = 3, the y-coordinate will change sign. So, the coordinates of the image of D will be (3, -6).
Therefore, the correct answer is (3, -6).
To reflect a point over a line, we can use the formula (x, y) -> (x, 2a - y), where a is the y-coordinate of a point on the line. In this case, the line y = 3 has a y-coordinate of 3.
Applying the formula to point D(3, 6), we get:
(x, y) -> (x, 2(3) - 6)
-> (x, 6 - 6)
-> (x, 0)
Therefore, the image of D(3, 6) after reflecting over the line y = 3 is (3, 0).
The correct answer is (3, 0).
To find the image of point D after reflecting the triangle over the line y = 3, we need to determine the new y-coordinate of D while keeping the x-coordinate unchanged.
First, let's find the line of reflection by finding the distance between the line y = 3 and point D. The distance between the two is the difference between the y-coordinate of point D and the equation of the line y = 3.
y-coordinate of D - equation of the line
6 - 3 = 3
Therefore, the distance between the line y = 3 and point D is 3 units.
Since the line of reflection is parallel to the x-axis, the x-coordinate of point D will remain the same.
Now, we need to determine whether the triangle is being reflected above or below the line y = 3.
The given triangle CDE has the y-coordinate of point D as 6, which is greater than the line y = 3. This means that after reflecting, the y-coordinate of the image of D will be less than 3.
To get the final coordinates of the image of D, we subtract the distance (3 units) from the y-coordinate of point D to reflect it below the line y = 3.
y-coordinate of D - distance
6 - 3 = 3
So, the image of point D after reflecting the triangle over the line y = 3 will have the coordinates (3, 3).
Therefore, the correct answer is (3, 3).