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 wxy 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:

Question 12

Step1: Recall isometry definition

Isometry is a transformation that preserves distance. Translation, rotation, and reflection are isometries as they keep the size and shape of the figure the same. Dilation changes the size of the figure.

Step2: Evaluate each option

Translation (I), rotation (II), and reflection (III) are isometries. Dilation (IV) is not. So the answer is the set of I, II, and III.

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's assume the original coordinates of X are \((x,y)\). The new coordinates \((x',y')\) will be \(x'=x + 5\) and \(y'=y-2\). Without seeing the original coordinates in the graph, we can't calculate exact values, but if we assume the original coordinates of \(X\) are \((- 4,3)\) (for example, if we had the graph details), then \(x'=-4 + 5=1\) and \(y'=3-2 = 1\). But based on the general rule and the options, if we assume the original coordinates of \(X\) are \((-2,5)\), then \(x'=-2+5 = 3\) and \(y'=5 - 2=3\). However, if we assume the original coordinates of \(X\) are \((-4,3)\) and follow the translation rule: new \(x=-4 + 5=1\) and new \(y=3-2 = 1\). If we assume the original coordinates of \(X\) are \((-2,3)\), new \(x=-2 + 5=3\) and new \(y=3-2 = 1\).

Step1: Understand translation properties

When a polygon is translated, it is just moved in the coordinate - plane. The size and shape of the polygon do not change.

Step2: Analyze each characteristic

Side lengths remain the same because translation is a rigid motion. Area remains the same as the size of the polygon doesn't change. The coordinates of the vertices change because the polygon is moved to a new position.

Answer:

A. I, II, and III

Question 13