Question

name zaylen franci 1. what transformation was used to generate figure b from figure a? period 6 a. clockwise rotation 90° about the origin b. counterclockwise rotation 90° about the origin c. translation 8 units to the left and 4 units up d. translations 3 units to the left and 1 unit down 2. a triangle has the vertices of (-2, 2), (12, -4), and (6, 10). if the triangle undergoes a dilation with a scale factor of one - half, what will be the new vertices of the image? a. (0, 4), (14, -2), (8, 12) b. (-4, 4), (24, -8), (12, 20) c. (-1, 1), (6, -2), (3, 5) d. (-6, 6), (6, -2), (8, 12) 3. describe a sequence of transformations that shows that polygon a is congruent to polygon b. 4. eight angles are formed in the diagram below. if the measure of ∠2 is 75°, what is the measure of 5. what is the measure of angle k?

Explanation:

1.

Step1: Observe orientation change

By looking at Figure A and Figure B, we see that the orientation of the figure has changed in a counter - clockwise manner by 90 degrees about the origin.

Step1: Apply dilation formula

The dilation formula for a point \((x,y)\) with a scale factor \(k\) is \((kx,ky)\). Here \(k = \frac{1}{2}\). For point \((- 2,2)\), the new point is \((\frac{-2}{2},\frac{2}{2})=(-1,1)\); for \((12,-4)\), it is \((\frac{12}{2},\frac{-4}{2})=(6, - 2)\); for \((6,10)\), it is \((\frac{6}{2},\frac{10}{2})=(3,5)\)

Step1: Identify translation

First, translate Polygon A so that one of its vertices coincides with a corresponding vertex of Polygon B.

Step2: Identify rotation

Then, rotate Polygon A about the coincided vertex until it matches Polygon B. For example, translate Polygon A down and to the right so that a bottom - left vertex of A coincides with the corresponding vertex of B, then rotate it 90 degrees clockwise.

Answer:

b. Counterclockwise rotation 90° about the origin
2.