**A strong positive, B weak positive, C weak neg, D fairly strong neg, E weak neg, F no correlation**
**Unit 5: Transformations in the Coordinate Plane**
**G.CO.1, 2, 3, 4, 5: Experiment with Transformations in the Plane**
199. Draw the image of this figure reflected across the x-axis. 200. Draw the image of this figure
reflected across y = 3.
201. Draw the image of this figure reflected 202. Draw the image of the figure using the translation
across y = 1. (x, y) (x + 4, y = 2)
203. Draw the image according to the rule and identify the transformation.
a) (x, y) (x – 2, y + 5) b) (x, y) (-x, -y)
**translation reflection over x and y axis, or rotate 180**
c) (x, y) (-x, y) d) (x, y) (x + 1, y + 4)
**reflection over y-axis translation right 1 and up 4**
204. Specify a sequence of transformations that will map the pre-image onto the image.
a) **reflect over x = -2** b) **reflect over x = 2**
c) **rotate 180** d) **translate down 2 and right 4**
205. Which transformation(s) map the hexagon onto itself? (think reflections and rotations)
**reflect over x and y-axis, or rotate 60**^{o}
206. Which transformation maps the trapezoid onto itself?
**reflection over y-axis, rotate 360**^{o}
207. IF the parallelogram below were translated 3 units left and 6 units down, what would be the coordinates of the new image W’X’Y’Z’?
**W’ (-2, -1) X’ (0, 3) Y’ (5, 3) Z’ (3, -1)**
208. To plan a scene in an animated movie, Roger rotates the below figure around point P by 90° in a clockwise direction. Which drawing shows the pre-image and the final image? **B**
a. **b**. c.
209. Use the diagram to answer the questions.
a) If X is reflected across line 3, where will it end up ? **B**
b) What sequence of transformations will map figure A onto figure B ?
**reflect over 5, then reflect over 3**
c) What sequence of transformations will map figure D onto figure C ?
**rotate 180, then translate 2 over**
d) If X is reflected across line 3 and then translated to the right, where will it be?
**C**
210. Which translation moves ABC to A’B’C’? 211. Which figure represents a rotation of figure 1?
**translate down 4 and right 8 Figure 3**
212. Draw the image of this figure if it is reflected across the y-axis, and then reflected over the x-axis.
**Unit 6 : Connecting Algebra and Geometry Through Coordinates**
**G.GPE.4, 5, 6, 7- Use coordinates to prove simple geometric theorems algebraically**
213. Line *m* is represented by the equation y = 2x + 3. What is the equation of the line that is perpendicular to line *m* and passes through the point (-6, 1) ?
**y = -1/2x - 2**
214. Given line *l* is y = 4x + 3, what is the equation of the line that is perpendicular to line *l* and runs through the point (2, -7) ?
**y = -1/4x – 6.5 or y = -1/4x – 13/2**
215. Write an equation of the line that is perpendicular to the line y = 2x + 8 and passes through the point (6, -2) .
**y = -1/2x + 1**
216. What is the equation of the line that is parallel to the line 5x + 20y = 10 and passes through the point (8, 3) ?
**y = -1/4x + 5**
217. Write an equation of the line that is parallel to the line 2x + 4y = 6 and goes through the point
(6, 4).
**y = -1/2x + 7**
218. Write an equation for the perpendicular bisector for the line segment shown in the graph.
**y = -11/2x – 63/4**
219. Write an equation of a line perpendicular to y = that passes through the point (2, -3).
**y = -3x + 3**
220. Determine if the point (-1, √7) lies on a circle centered at the origin and containing the point (3, 0).
**No, but if i twas (-1, √8) it would !**
221. Determine if the point (4, 5) lies on a circle centered at (2, 2) and containing the point (2, -2).
**no**
222. Determine if the point (0, √3) lies on a circle centered at (-1, 3) and containing the point (-1, 1).
**no**
223. Rectangle ABCD has coordinates A(1, 1), B(1, 3), C(4, 3). Find the coordinates of D.
**D (4, 1)**
224. Prove that EFGH is a rhombus if the vertices given are E(-2, 3), F(0, 4), G(2, 3), H(0, 2).
**all 4 sides equal, d = √5**
225. The coordinates for the vertices of a right triangle are (1, 4), (6, 4), (6, 1). Calculate the area of the right triangle. Calculate the perimeter of the right triangle.
**P = 8 + √34 or 13.8 ; A = 7.5**
226. Classify the quadrilateral LMNO with vertices L(-3, 4), M(3, 3), N(5, 7), and O(-1, 8).
Then, prove that the **diagonals bisect each other**. What formula do you use ?
**parallelogram, sides are √37 and 3√2, use distance formula to prove diagonals bisect**
227. Determine the most precise name for the quadrilateral shown. How can you PROVE it ?
**rhombus, all sides are √5 using distance formula**
228. A rhombus has vertices at (0, 0), (1, 4), (5, 5), and (4, 1). Prove that the diagonals of the rhombus are perpendicular. Prove that all 4 sides are congruent. Then find the **perimeter**.
**use slope to prove perpendicular : (5, 5) and (0, 0) slope is 1, (1, 4) and (4, 1) slope is -1, so they are negative reciprocals ; sides measure √17 ; P = 4√17 or 16.5**
229. Classify the quadrilateral with vertices P(-2, 1), A(1, 4), R(4, 1), and T(1, -2). Prove it using coordinate geometry (distance, slope). Then, find the **perimeter **and **area**.
**square, sides are 3√2 and perpendicular ; P = 12√2 or 17 and A = 18**
230. Find the point, M, that divides segment AB into a ratio of if A is at (0, 15) and B is at (20, 0).
**(12, 6)**
231. Find the point, M, that divides segment AB into a ratio of 5:2 if A is at (-1, 2) and B is at (8, 15).
**(38/7, 79/7)**
232. Given the points P(-4, -2) and Q(4, -10), what are the coordinates of the point on directed line segment PQ that partitions PQ in the ratio 4:1?
**(12/5, -42/5)**
233. Given the points A(-4, -2) and B(4, -10), what are the coordinates of the point on directed line segment AB that partitions AB in the ratio ?
**(1, -7)**
234. Given the points A(-33, 0) and B(0, 44), find the coordinates of the point P on directed line segment AB that partitions AB in the ratio ?
**(-21, 16)**
235. Given the points P(2, 3) and Q(5, 9), find the coordinate M that partitions directed line segment PQ in a ratio of 1:2.
**(3, 5)**
236. Find the coordinate, T, that divides AB into a ratio of 3:1 if A is at (-1, -6) and B is at (-5, 2).
**(-4, 0)**
237. Find the coordinate, T, that partitions segment AB in a ratio of if A is (2, -2) and B is (-3, 8).
**(-1, 4)**
238. Find the coordinate, T, that divides AB into a ratio of 2:1 if A is at (-1, 2) and B is at (5, 12).
**(3, 26/3)**
239. Triangle ABC has vertices at (2, 4), (-5, -3), and (2, -3). Find the **perimeter** and **area** of the triangle.
**P = 14 + 7√2 or 23.9 and A = 24.5**
240. Find the **perimeter** and **area** of rectangle with vertices A(-5, 0), B(3, 2), C(-4, -4), D(4, -2).
**P = 6√17 or 24.7 and A = 34**
241. Given a rectangle with vertices E(-3, 5), F(1, 4), G(-1, -4), H(-5, -3), calculate the **perimeter **and **area** of the rectangle. Then use distance formula to prove the diagonals bisect each other.
**P = 6√17 or 24.7 and A = 34; use distance formula to prove diagonals bisect by finding the two distances and proving they’re the same**
242. Classify the quadrilateral with vertices at (-5, 3), (3, 5), (5, -3), and (-3, -5). Then find the **perimeter and area** of the quadrilateral.
**Square, P = 8√17 or 33 and A = 68**
243. Classify the quadrilateral with vertices at (-5, 2), (-1, 4), (4, -1), and (-4, -5). Then find the **perimeter ** of the figure.
**trapezoid (slopes are parallel, m = ½); P = 6√5 + 10√2 or 27.6**
244. Quadrilateral ABCD has vertices at A(-3, 4), B(3, 2), C(5, -4), and D(-1, -2). What type of quadrilateral is ABCD? How do you know? What is the perimeter of ABCD?
**rhombus because all sides 2√10; P = 8√10 or 25.3**
245. A triangle has vertices at (9, 15), (20, 13), and (20, 5). Calculate the **perimeter** and **area** of the triangle.
**sides are 8, 5√5, and √221; P = 34.0 and A = 20√5 or 44.7**
246. Triangle ABC has vertices shown. What is the **area** and **perimeter** of the triangle?
**sides are √68 for 2 legs and 2√34 for hypotenuse; A = 34; P = 2√34 + 4√17 or 28.2**
247. Use the graph to calculate the **area **and **perimeter **of the triangle shown.
**sides are 3, 4, 5; P = 12 and A = 6**
248. Triangle PQR has vertices at P(-3, 1), Q(1, 3), and R(3, -2). Find the perimeter and area of the triangle.
**sides are 3√5, 2√5, and √29 ; P = √29 + 5√5 or 16.6 and A = √145 or 12.0**
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