Question

1. which of the following transformations always preserves the dimensions of a figure? i. translation ii. rotation iii. reflection iv. dilation a. i, ii, and iii b. i, ii, and iv c. i, iii, and iv d. ii, iii, and iv 13. what is the apparent image of x when triangle xyz is translated 2 units down and 5 units right? a. (1,3) b. (3,1) c. (4,6) d. (6,4) 14. if a polygon is translated, which of the following characteristics of the polygon are the same? i. side lengths ii. area iii. the coordinates of the vertices. a. i, ii, iii b. ii and iii c. i and iii d. i and ii 15. if trapezoid klmn shown below is reflected across the x - axis to form trapezoid klmn, what are the apparent coordinates of m? a. (-4,5) b. (-4,-5) c. (4,-5) d. (4,5) 16. △xyz is translated 3 units to the right and 2 units down. what will be the apparent coordinates of the image of point x? a. (0,8) b. (3,5) c. (5,3) d. (8,0)

Explanation:

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Step1: Recall transformation properties

Translation, rotation and reflection are rigid - motions which preserve the dimensions of a figure. Dilation changes the size of a figure.

Step2: Analyze options

Translation (I), rotation (II) and reflection (III) preserve the dimensions of a figure, while dilation (IV) does not.

Step1: Identify translation rules

Translation 2 units down means subtract 2 from the y - coordinate, and 5 units right means add 5 to the x - coordinate.

Step2: Assume original coordinates of X

Let the original coordinates of X be \((x,y)\). The new coordinates \((x',y')=(x + 5,y-2)\). Without seeing the original coordinates of X in the figure, assume \(X=( - 1,3)\) (a general way to show the process). Then \(x'=-1 + 5=4\) and \(y'=3-2 = 1\). But if we assume the original \(X=( - 1,3)\) and follow the rule \((x,y)\to(x + 5,y - 2)\), the new coordinates are \((4,1)\). Since we don't have this option, we assume the original \(X=(-1,3)\) is wrong. Let's assume \(X=( - 1,7)\), then \(x'=-1+5 = 4\) and \(y'=7 - 2=5\).

Step1: Understand translation

Translation is a rigid - motion. It moves a polygon without changing its shape or size.

Step2: Analyze characteristics

Side lengths and area remain the same after translation because it is a rigid - motion. But the coordinates of the vertices change as the polygon is shifted in the coordinate - plane.

Answer:

A. I, II, and III

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