Given C(2,-8),D(-6,4),E(0,4),U(1,-4),V(-3,2), and W(0,2), and that /_\CDE is the preimage of /_\UVW, represent the transformation algebraically. (x,y)rarr(◻x,◻y)

Question

Given  C(2,-8),D(-6,4),E(0,4),U(1,-4),V(-3,2), and  W(0,2), and that  /_\CDE is the preimage of  /_\UVW, represent the transformation algebraically.  (x,y)rarr(◻x,◻y)

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Analyze Coordinates: To solve this problem, we need to find the transformation that maps triangle CDE to triangle UVW. We will start by comparing the coordinates of the corresponding points to determine the transformation.X-Coordinate Comparison: Let's first look at the x-coordinates of the corresponding points. We can compare the x-coordinates of C and U, D and V, E and W to find a pattern. C(2) -> U(1), D(-6) -> V(-3), E(0) -> W(0). It seems that the x-coordinate of the image is half the x-coordinate of the preimage. This suggests a scaling transformation with a scale factor of 1/2 in the x-direction.Y-Coordinate Comparison: Now let's look at the y-coordinates of the corresponding points. We can compare the y-coordinates of C and U, D and V, E and W to find a pattern. C(-8) -> U(-4), D(4) -> V(2), E(4) -> W(2). It seems that the y-coordinate of the image is half the y-coordinate of the preimage. This suggests a scaling transformation with a scale factor of 1/2 in the y-direction as well.Algebraic Representation: Since both the x and y-coordinates are scaled by a factor of 1/2, the transformation can be represented algebraically as: (x, y) -> (1/2 * x, 1/2 * y). This transformation scales any point by a factor of 1/2 in both the x and y directions.Transformation Verification: To check for any math errors, we can apply the transformation to one of the points in triangle CDE and see if we get the corresponding point in triangle UVW. Let's apply it to point C(2, -8): (1/2 * 2, 1/2 * -8) = (1, -4), which is point U, as expected. No math errors are detected.

Given $C(2,-8),D(-6,4),E(0,4),U(1,-4),V(-3,2),$ and $\newline$ $W(0,2)$ , and that $\angle CDE$ is the preimage of $\angle UVW$ , represent the transformation algebraically. $\newline$ $(x,y)\rightarrow(\square x,\square y)$

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