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?
all your x's will stay the same
for D(3.6), D is 3 units above y = 3
so the reflection in y = 3 would put it 3 units below,
resulting in D1(3,0)
To find the coordinates of the image of point D after reflecting over the line y = 3, we need to follow these steps:
1. Determine the line of reflection: In this case, the line of reflection is y = 3.
2. Find the distance between D and the line of reflection: The distance between a point (x, y) and a line ax + by + c = 0 is given by the formula:
distance = |ax + by + c| / sqrt(a^2 + b^2)
In our case, the line of reflection is y = 3, which can be written as y - 3 = 0. So, a = 0, b = 1, and c = -3.
The distance between point D(3, 6) and the line y - 3 = 0 is:
distance = |0 * 3 + 1 * 6 - 3| / sqrt(0^2 + 1^2)
distance = |6 - 3| / 1
distance = 3 / 1
distance = 3
3. Find the image of D: Since the line of reflection is horizontal, the image of D will have the same x-coordinate as D but a y-coordinate that is 3 units away from the line of reflection. D is above the line y = 3, so its image will be below the line whose y-coordinate is 3 units less than the y-coordinate of D.
The y-coordinate of D is 6, and the distance between D and the line y = 3 is 3 units. So, the y-coordinate of the image of D will be 6 - 3 = 3.
Therefore, the coordinates of the image of D after reflecting over the line y = 3 are (3, 3).