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- T^2 is the torus, RP^2 is the real projective planeA transformation maps quadrilateral ABCD onto quadrilateral A' B'C' D' The coordinates of A'B'C'D' are: (-1,0), (-3,3), (-4,2), (-8,1). Which composition of isometries can be used to show that ABCD A'B'C'D? 6 5 4 3 2 1- 0 -1- -2₁- A 1 2 B 3 C 4 5 6 O A counterclockwise rotation of 270 degrees. O A reflection across the x axis and a translation of one unit up. O A reflection across the y axis and a translation of one unit down. O A translation one unit down and a reflection across the x axis. D 7 8Find all points having an x-coordinate of 1 whose distance from the point (- 3, - 2) is 5. ..... The point(s) is(are) (Type an ordered pair. Use a comma to separate answers as needed.) nap (9) Textbook ulus - Fall 2021) is based on Sullivan: Precalculus, 11e Copyright © 2021 Pearson Education Inc. All Rights Reserved. NZXT
- Neatly sketch the set of points {(r,e): 3Let S be a set of five distinct points in the plane with integer coordinates. Show that the midpoint of the segment joining at least one pair of these points has integer coordinates.) Consider the space R^2 equipped with the sunflower metric. Identify explicitly the set of points in R 2 which forms the ball B1((2, 2)) of radius 1 and centre at the point (2, 2). Provide reasons for your answer.a quutiont of a compact space is compact compact nd connected. Show that connectedShow that Ris not compact for the Standard topology compact for the cofinite topology. but is compact for theAll parts, please. I will post the 8.7 and 9.3 exercises below. The parts are labeled in the image 8.7 says Consider the real Cartesian plane R^2, with lines and betweenness as before (Example 7.3.1), but define a different notion of congruence of line segments using the distance function given by the sum of the absolute values: d(A,B) = |a1-b1| + |a2-b2|, where A = (a1,a2) and B = (b1,b2). Some people call this "taxicab geometry" because it is similar to the distance by taxi from one point to another in a city where all streets run east-west or north-south. Show that the axioms (C1), (C2), (C3) hold, so that this is another model of the axioms introduced so far. What does the circle with center (0,0) and radius 1 look in this model? 9.3 says Consider the real Cartesian plane where congruence of line segments is given by the absolute value distance function (Exercise 8.7). Using the usual congruence of angles that you know from analytic geometry (Section 16), show that (C4) and (C5)…
