Question

1. ( abcdecong pqrst )

part 1: ( abcde ) can be mapped onto ( pqrst ) by...
a rotation
b reflection
c translation
d the figures are not congruent.
part 2: the coordinate notation is

Explanation:

Part 1:

Step 1: Recall the properties of congruent figures

Congruent figures have the same shape and size. Transformations like rotation, reflection, and translation preserve the shape and size of a figure.

Step 2: Analyze each transformation

• Rotation: A rotation turns a figure around a point. It does not change the size or shape of the figure. So, \(ABCDE\) can be mapped onto \(PQRST\) by rotation.
• Reflection: A reflection flips a figure over a line. It does not change the size or shape of the figure. So, \(ABCDE\) can be mapped onto \(PQRST\) by reflection.
• Translation: A translation slides a figure. It does not change the size or shape of the figure. So, \(ABCDE\) can be mapped onto \(PQRST\) by translation.

Part 2:

Since the problem does not provide specific coordinates to write in coordinate - notation, we assume a general approach.
If we consider a translation, for example, if we assume a point \(A(x_1,y_1)\) in \(ABCDE\) and its corresponding point \(P(x_2,y_2)\) in \(PQRST\), the translation vector \(\vec{v}=(x_2 - x_1,y_2 - y_1)\). But without specific coordinate values for the vertices of the polygons, we can't give a numerical coordinate - notation. However, if we assume a rotation about the origin (for simplicity, if the center of rotation is the origin) with an angle \(\theta\), a point \(A(x,y)\) in \(ABCDE\) is transformed to \(A'(x\cos\theta - y\sin\theta,x\sin\theta + y\cos\theta)\) in \(PQRST\). Or for a reflection over the \(x\) - axis, a point \(A(x,y)\) is transformed to \(A'(x, - y)\) (if the reflection is over the \(x\) - axis) etc.

Answer:

Part 1: A. Rotation, B. Reflection, C. Translation
Part 2: If it is a translation, for a general point \(A(x,y)\) in \(ABCDE\) and its image \(P(x + a,y + b)\) in \(PQRST\), the coordinate - notation is \((x,y)\to(x + a,y + b)\). If it is a rotation about the origin by an angle \(\theta\), \((x,y)\to(x\cos\theta - y\sin\theta,x\sin\theta + y\cos\theta)\). If it is a reflection over the \(x\) - axis \((x,y)\to(x, - y)\), over the \(y\) - axis \((x,y)\to(-x,y)\) (coordinate - notations vary depending on the type of transformation and its parameters).