Which coordinate notation describes the result of a translation of the point (-1,2) left 5 units followed by a reflection over the line y=0?

(x,y)→(x-5,y)

(x,y)→(y,x-5)

(x,y)→(x-5,-y)

(x,y)→(x+5,-y)

Let's break the problem down step by step:

1. **Translation left by 5 units**: 
   When you move a point left, the x-coordinate decreases by the number of units moved. So, translating the point \((-1, 2)\) left by 5 units will affect only the x-coordinate:
   \[
   (-1 - 5, 2) = (-6, 2)
   \]

2. **Reflection over the line \(y = 0\)**:
   The line \(y = 0\) is the x-axis. Reflecting a point over the x-axis (the line \(y = 0\)) changes the sign of the y-coordinate while leaving the x-coordinate unchanged. So:
   \[
   (-6, -2)
   \]

Therefore, the transformation we applied to the point \((-1, 2)\) can be described as:

\[
(x, y) \to (x - 5, -y)
\]

The correct coordinate notation is: 

**\((x, y) \to (x - 5, -y)\)**.

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Do you want more details or have any questions?

Here are 5 related questions for further practice:
1. What happens to a point after a translation up by 4 units?
2. How would a point translate if it moved 7 units to the right?
3. What is the result of reflecting a point over the line \(x = 0\)?
4. How do you describe a reflection over the line \(y = x\)?
5. What is the formula for a 90-degree clockwise rotation of a point?

**Tip:** Always apply transformations step by step to avoid confusion, especially when combining multiple transformations.

Which coordinate notation describes the result of a translation of the point (-1,2) left 5 units followed by a reflection over the line y=0?

Learn how to solve a translation and reflection problem involving point (-1,2). This problem explains step-by-step how to translate the point left by 5 units and reflect it over the x-axis (y=0). It covers important coordinate geometry concepts and rules for students in Grades 6-8.

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