Question

1. complete the statement that describes the series of transformations mapping \\( \triangle m o p \\) onto \\( \triangle q r s \\) in the diagram below.

\\( m o p \\) is

\\( \

$$\begin{array} { l } { \\text { (a) reflected over } x = 0 } \\\\ { \\text { (b) reflected over } y = 0 } \\\\ { \\text { (c) rotated } 90 \\text { degrees } } \\\\ { \\text { counterclockwise. } } \\\\ { \\text { (d) translated } 5 \\text { units vertically } } \\\\ { \\text { and } 5 \\text { units horizontally } } \\end{array}$$

\\)

then

\\( \

$$\begin{array} { l } { \\text { (a) reflected over } x = 0. } \\\\ { \\text { (b) reflected over } y = 0. } \\\\ { \\text { (c) rotated } 180 \\text { degrees. } } \\\\ { \\text { (d) translated } 2 \\text { units vertically } } \\\\ { \\text { and } 2 \\text { units horizontally. } } \\end{array}$$

\\)

Explanation:

Step1: Analyze reflection

The line \(x = 0\) is the \(y -\)axis. Reflecting \(\triangle MOP\) over the \(y -\)axis ( \(x=0\)) changes the \(x -\)coordinates of the points. For example, if a point \((x,y)\) in \(\triangle MOP\) is reflected over \(x = 0\), it becomes \((-x,y)\).

Step2: Analyze translation

After reflection, we need to check the vertical and horizontal movement. Counting the vertical and horizontal displacements:

• Vertically: The \(y -\)coordinate of the lowest - point of \(\triangle MOP\) (after reflection) is moved down. The vertical displacement is \(2\) units (e.g., if we consider the \(y -\)coordinate of point \(P\) after reflection and then compare to the corresponding point in \(\triangle QRS\)).
• Horizontally: The \(x -\)coordinate of the reflected triangle is moved \(2\) units to the right.

Answer:

\(\triangle MOP\) is reflected over \(x = 0\) then translated \(2\) units vertically and \(2\) units horizontally.