The coordinates of the vertices of triangle 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?
I think (3,-6), but not real sure.
think of folding the diagram on the line y=3. x-values don't change, and y-values are moved the same distance from the line y=3.
The distance of (x,y) from (x,3) is y-3.
so, (x,y) --> (x,3-(y-3)) = (x,6-y)
(3,6) --> (3,0)
D is 3 units above the line y=3, so it moves to 3 units below the line, or y=0.
dats correct O: howd you know <3
If triangle ABC is reflected across the y-axis, what are the coordinates of A'?
To find the coordinates of the image of point D after reflecting the triangle CDE over the line y=3, you need to follow these steps:
1. Identify the line of reflection: In this case, the line of reflection is y=3.
2. Find the distance between the original point and the line of reflection: To do this, subtract the y-coordinate of the original point from the equation of the line of reflection. In this case, the y-coordinate of point D is 6, and the equation of the line of reflection is y=3. So, the distance between D and the line of reflection is 6-3=3.
3. Determine the direction of the reflection: Since the distance between D and the line of reflection is positive (3), the reflection will occur on the opposite side of the line of reflection.
4. Reflect the y-coordinate of point D: To reflect the y-coordinate of D, you need to subtract the distance (3) from the y-coordinate of the line of reflection. The y-coordinate of the line of reflection is 3, so the reflected y-coordinate of D is 3-3=0.
5. Keep the x-coordinate the same: The x-coordinate of D remains the same because the line of reflection is vertical and does not affect the x-coordinate.
Therefore, the coordinates of the image of D after reflecting the triangle CDE over the line y=3 are (3, 0).