Question

a composition of transformations maps \\( \triangle k l m \\) to \\( \triangle k^{prime prime} l^{prime prime} m^{prime prime} \\).
the first transformation for this composition is
\\_\\_\\_\\_\\_\\_\\_\\_, and the second transformation is a
translation down and to the right.
\\( \bigcirc \\) a \\( 90^{\circ} \\) rotation about point l
\\( \bigcirc \\) a \\( 270^{\circ} \\) rotation about point l
\\( \bigcirc \\) a \\( 90^{\circ} \\) rotation about point p
\\( \bigcirc \\) a \\( 270^{\circ} \\) rotation about point p

Explanation:

Step1: Analyze rotation direction and center

• Observe the position of \(\triangle KLM\) and \(\triangle K'L'M'\).
• The rotation is about point \(L\) (not \(P\)) as \(L\) is a common vertex in the first - stage transformation.
• A \(90^{\circ}\) rotation about a point \(O\) in the counter - clockwise direction changes the orientation of the figure. If we consider the right - hand rule (for a standard coordinate system - like orientation of the plane of the triangles), a \(90^{\circ}\) rotation about \(L\) will map \(\triangle KLM\) to \(\triangle K'L'M'\) in the correct orientation. A \(270^{\circ}\) rotation about \(L\) would be equivalent to a \( - 90^{\circ}\) rotation (clockwise) and would not give the correct orientation as per the figure.

Answer:

a \(90^{\circ}\) rotation about point \(L\)