Answer:
The image is (0 , -6)
Step-by-step explanation:
* Lets explain some important facts
- When a point reflected across a line the perpendicular
distance from the point to the line equal the perpendicular
distance from its image to the same line
- If the line of the reflection is horizontal then the perpendicular
distance between the point and the line is y - y1 , and the
perpendicular distance between the image and the line is y2 - y
- If point (x , y) reflected across the x- axis, then its image is (x , -y)
* Lets solve the problem
∵ Point (0 , 0) reflected across the line y = 3
∴ y = 3 and y1 = 0
∴ The distance between the point and the line is 3 - 0 = 3
∴ The distance between the image and the line also = 3
∴ y2 - 3 = 3 ⇒ add 3 to both sides
∴ y2 = 6
∴ The y-coordinate of the image is 6
∴ The image of point (0 , 0) after reflection across the line y = 3 is (0 , 6)
- The image of the point reflected across the x-axis, then change the
sign of the y-coordinate
∴ The final image of point (0 , 0) is (0 , -6)
* The image is (0 , -6)
