Which shows the correct coordinates for the reflection of the point over the line y = -4
a. (-6,9)->(-6, 17)
b. (-6,9)->(6,-17)
c. (-6,9)->(-10,-9)
d. (-6,9)->(2,-9)
I how to reflect over a line. Can you help me please?
Of course! To reflect a point over a line, you can follow these steps:
1. Determine the equation of the line of reflection. In this case, the line of reflection is y = -4.
2. Find the distance between the point and the line of reflection, which is the vertical distance from the point to the line. You can calculate this distance using the formula: distance = y-coordinate of the point - y-coordinate of the line of reflection.
3. Reflect the point by adding twice the distance calculated in step 2 to the y-coordinate of the line of reflection.
Let's apply these steps to the given point (-6, 9) and the line y = -4:
1. The equation of the line of reflection is y = -4.
2. The distance between the point (-6, 9) and the line y = -4 is: distance = 9 - (-4) = 13.
3. To reflect the point, we add twice the distance to the y-coordinate of the line of reflection: -4 + 2(13) = 22.
Therefore, the reflection of the point (-6, 9) over the line y = -4 is (x, y) = (-6, 22).
Now let's check the answer choices:
a. (-6, 9) -> (-6, 17): This is not the correct reflection.
b. (-6, 9) -> (6, -17): This is not the correct reflection.
c. (-6, 9) -> (-10, -9): This is not the correct reflection.
d. (-6, 9) -> (2, -9): This is not the correct reflection.
None of the given answer choices show the correct coordinates for the reflection of the point (-6, 9) over the line y = -4. I hope this explanation helps!