Chapter PS, Problem 4.4P

To determine

To find: The original coordinates of the point.

Answer to Problem 4.4P

(5, -2)

Explanation of Solution

Given:

A point reflected across $x$ axis, then moved up three units and two units to the left. Final coordinates of the point are (3, 5).

  

Let the original coordinates of the point be ( $x,y$ ).

After taking mirror image across $x$ axis, the $y$ coordinate becomes negative.

Therefore, the coordinate becomes ( $x,-y$ ).

Now, it is shifted three units up and two units left. It means three units added to $y$ coordinate and two units subtracted from $x$ coordinate.

Therefore, the coordinate becomes ( $x-2,-y+3$ ) which is given as (3, 5).

Comparing the values:

  $\begin{array}{l}x-2=3\Rightarrow x=5\\ -y+3=5\Rightarrow y=-2\end{array}$