Answer:
The coordinates of the image of point A are (-1, -6)
Step-by-step explanation:
Let us revise the rule of translation to the left, down, and reflection across the x-axis
- If the point (x, y) translated horizontally to the left by h units then its image is (x - h, y) ⇒ T (x, y) → (x - h, y)
- If the point (x, y) translated vertically down by k units then its image is (x, y - k) ⇒ T (x, y) → (x, y - k)
- If the point (x, y) reflected across the x-axis, then its image is (x, -y), the rule of reflection is rx-axis (x, y) → (x, -y)
∵ The coordinates of point A are (3, 4)
∵ It is translated 4 units left
∴ h = 4
→ By using the 1st rule above
∴ Its image is (3 - 4, 4)
∴ Its image is (-1, 4)
∵ Its is reflected across the x-axis
→ By using the 3rd rule above change the sign of its y-coordinate
∴ The new image is (-1, -4)
∵ It is translated 2 units down
∴ k = 2
→ By using the 2nd rule above
∴ The final image is (-1, -4 - 2)
∴ The final image is (-1, -6)
∴ The coordinates of the image of point A are (-1, -6).
