Determine a series of trans form ation s that would map Figure I onto Fig ure J.

To map Figure I onto Figure J using transformations, we need to determine the sequence of transformations that will take the vertices of Figure I to the corresponding vertices of Figure J. Let's analyze the given coordinates of both figures and plan our transformations step by step.Step 1: Identify the corresponding verticesWe need to match the vertices of Figure I to the vertices of Figure J. Since the question does not specify which vertices correspond to each other, we will assume that the vertices are listed in a corresponding order. This means that the first vertex of Figure I corresponds to the first vertex of Figure J, and so on.Step 2: Determine the translationThe first transformation we will apply is a translation (a slide) to move Figure I to the general vicinity of Figure J. We can do this by finding the difference between the x-coordinates and y-coordinates of the corresponding vertices of Figures I and J.Let's use the first vertices of Figures I and J to find the translation vector:Figure I first vertex: (-9, -2)Figure J first vertex: (-1, 7)Translation vector = (Figure J vertex) - (Figure I vertex)Translation vector = (-1 - (-9), 7 - (-2))Translation vector = (8, 9)So, we need to translate Figure I by 8 units to the right and 9 units up.Step 3: Determine the scale factorAfter translating Figure I, we need to check if the figures are of the same size or if we need to scale Figure I. To do this, we can compare the distances between corresponding vertices before and after the translation.Let's use the distance between the first and second vertices of Figure I and Figure J to find the scale factor:Figure I distance: √((-8 - (-9))^2 + (-4 - (-2))^2) = √((1)^2 + (-2)^2) = √(1 + 4) = √5Figure J distance: √((2 - (-1))^2 + (8 - 7)^2) = √((3)^2 + (1)^2) = √(9 + 1) = √10Scale factor = √10 / √5 = √(10/5) = √2So, we need to scale Figure I by a factor of √2.Step 4: Determine the rotation (if necessary)After translating and scaling, we need to check if Figure I needs to be rotated to match Figure J. We can do this by comparing the orientation of the figures.Since the question does not provide information about the orientation of the figures, we will assume that no rotation is necessary if the figures are not rotated relative to each other. If they are, we would need to determine the angle of rotation by comparing the angles between corresponding line segments of Figures I and J.Step 5: Determine the reflection (if necessary)Finally, we need to check if a reflection is needed. This can be determined by observing the orientation of the figures after the translation and scaling. If Figure I is a mirror image of Figure J, then a reflection across the appropriate axis is required.Since the question does not provide information about the orientation of the figures, we will assume that no reflection is necessary if the figures have the same handedness. If they are mirror images, we would need to reflect Figure I across the appropriate axis.Final Answer:To map Figure I onto Figure J, we need to:1. Translate Figure I by the vector (8, 9).2. Scale Figure I by a factor of √2.3. If necessary, rotate Figure I by the appropriate angle (not determined due to lack of information).4. If necessary, reflect Figure I across the appropriate axis (not determined due to lack of information).