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?
(3, –6)
(3, –3)
(3, 0)
(3, 9)
(x,y) --> (x,6-y)
D: (3,6) --> (3,0)
To find the coordinates of the image of D after reflecting it over the line y = 3, you need to understand how to reflect points over a line.
When reflecting a point over a line, you can follow these steps:
1. Find the perpendicular distance between the given point and the line of reflection.
2. Extend that distance in the opposite direction from the given point to find the new reflected point.
In this case, the line of reflection is y = 3. So, let's follow these steps to find the image of D.
Step 1: Calculate the perpendicular distance between D(3, 6) and the line y = 3.
- The perpendicular distance is the difference between the y-coordinate of the given point and the y-coordinate of the line of reflection.
- In this case, the perpendicular distance would be 6 - 3 = 3 units.
Step 2: Extend the perpendicular distance in the opposite direction from D(3, 6) to find the image of D.
- Since the perpendicular distance is positive, we need to extend it downwards from D.
- Subtract the perpendicular distance from the y-coordinate of D to get the y-coordinate of the image.
- The x-coordinate of the image remains the same as the x-coordinate of D.
- Therefore, the image of D would have coordinates (3, 6 - 3) = (3, 3).
So, the correct answer is (3, 3).