## What are we learning ?

**Competency in Focus:** Slope of straight line.

This problem is based on slope of straight line from American Mathematics contest (AMC 10B, 2012). It includes image formation due to reflection from a line of A point.

## First look at the knowledge graph.

## Next understand the problem

The point in the xy-plane with coordinates $(1000, 2012)$ is reflected across the line $y = 2000$. What are the coordinates of the reflected point? $\textbf{(A)}\ (998,2012)\qquad\textbf{(B)}\ (1000,1988)\qquad\textbf{(C)}\ (1000,2024)\qquad\textbf{(D)}\ (1000,4012)\qquad\textbf{(E)}\ (1012,2012)$

##### Source of the problem

American Mathematical Contest 2012, AMC 10B Problem 3

##### Key Competency

Slope of the Sriaght line

##### Difficulty Level

4/10

##### Suggested Book

Challenges and Thrills in Pre College Mathematics Excursion Of Mathematics

### Start with hints

Do you really need a hint? Try it first!

The line $y = 2000$ is a horizontal line located $12$ units beneath the point $(1000, 2012)$. When a point is reflected about a horizontal line, only the $y$ – coordinate will change.

The $x$ – coordinate remains the same. Since the $y$-coordinate of the point is $12$ units above the line of reflection, the new $y$ – coordinate will be $2000 – 12 = 1988$. Thus, the coordinates of the reflected point are $(1000, 1988)$.

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