Question

identify the transformation shown. for a challenge, also find a sequence of transformations for 7, 8, 10, 11.

Explanation:

Problem 7:

Step1: Observe Symmetry

The figure shows a reflection over the \( y \)-axis (or a vertical line of symmetry) as points like \( B \) and \( B' \), \( X \) and \( X' \) are mirror images across the \( y \)-axis. Also, there might be a translation or reflection - but primary is reflection over \( y \)-axis.

Step2: Sequence (Challenge)

First, reflect the original figure over the \( y \)-axis. Then, check for any translation, but in this case, the main transformation is reflection over \( y \)-axis.

Step1: Identify Movements

The triangle \( PMW \) to \( P'M'W' \): First, translate horizontally (right) and vertically (up), then maybe check for congruence (since shape and size same, so translation).

Step2: Calculate Translation

Count the grid units: From \( P \) to \( P' \): move right (let's say) 6 units and up 3 units (approx, based on grid). So translation: \((x,y)\to(x + 6,y + 3)\) (or similar, depending on grid).

Step1: Observe Position Change

The quadrilateral \( LJAM \) (top) to \( LJAM \) (bottom): It's a translation down (and left? Wait, looking at axes: the top figure is above the \( x \)-axis, bottom is below? Wait, no, the axes: the top has \( y \)-axis on right, bottom has \( x \)-axis? Wait, maybe reflection over \( x \)-axis and translation? Wait, better: the figure is translated down (vertical shift) and left (horizontal shift). Wait, actually, the coordinates: let's see points \( A \), \( L \), \( J \), \( M \): top \( A \) is at some \( (x,y) \), bottom \( A \) is at \( (x - a,y - b) \). So translation: vertical and horizontal shift.

Step2: Determine Translation

Count grid: From top \( A \) to bottom \( A \): move left (say) 0 (wait, no, axes: top figure has \( y \)-axis on right, bottom has \( x \)-axis on right? Wait, maybe reflection over \( x \)-axis? No, shape is same. Wait, actually, it's a vertical translation down (and horizontal left? No, the bottom figure is to the left and down. So translation: left and down.

Answer:

Transformation: Reflection over the \( y \)-axis.
Sequence (if needed): Reflection over \( y \)-axis.

Problem 8: