xy−9−8−7−6−5−4−3−2−1123456789−9−8−7−6−5−4−3−2−112345678921. For each point given in Exercise20above•Identify the quadrant or axis in/on which the point lies.•Find the point symmetric to the given point about thex-axis.•Find the point symmetric to the given point about they-axis.•Find the point symmetric to the given point about the origin.
16Relations and FunctionsIn Exercises22-29, find the distancedbetween the points and the midpointMof the line segmentwhich connects them.22. (1,2), (−3,5)23. (3,−10), (−1,2)24.12,4,32,−125.−23,32,73,226.245,65,−115,−195.27.(√2,√3),(−√8,−√12)28.(2√45,√12),(√20,√27).29. (0,0), (x, y)30. Find all of the points of the form (x,−1) which are 4 units from the point (3,2).31. Find all of the points on they-axis which are 5 units from the point (−5,3).32. Find all of the points on thex-axis which are 2 units from the point (−1,1).33. Find all of the points of the form (x,−x) which are 1 unit from the origin.34. Let’s assume for a moment that we are standing at the origin and the positivey-axis pointsdue North while the positivex-axis points due East.Our Sasquatch-o-meter tells us thatSasquatch is 3 miles West and 4 miles South of our current position. What are the coordinatesof his position? How far away is he from us? If he runs 7 miles due East what would his newposition be?35. Verify the Distance Formula1.1for the cases when:(a) The points are arranged vertically. (Hint: UseP(a, y0) andQ(a, y1).)(b) The points are arranged horizontally. (Hint: UseP(x0, b) andQ(x1, b).)(c) The points are actually the same point. (You shouldn’t need a hint for this one.)36. Verify the Midpoint Formula by showing the distance betweenP(x1, y1) andMand thedistance betweenMandQ(x2, y2) are both half of the distance betweenPandQ.37. Show that the pointsA,BandCbelow are the vertices of a right triangle.(a)A(−3,2),B(−6,4), andC(1,8)(b)A(−3,1),B(4,0) andC(0,−3)38. Find a pointD(x, y) such that the pointsA(−3,1),B(4,0),C(0,−3) andDare the cornersof a square. Justify your answer.39. Discuss with your classmates how many numbers are in the interval (0,1).40. The world is not ﬂat.12Thus the Cartesian Plane cannot possibly be the end of the story.Discuss with your classmates how you would extend Cartesian Coordinates to represent thethree dimensional world. What would the Distance and Midpoint formulas look like, assumingthose concepts make sense at all?12There are those who disagree with this statement. Look them up on the Internet some time when you’re bored.
20Relations and Functions1.2RelationsFrom one point of view,1all of Precalculus can be thought of as studying sets of points in the plane.With the Cartesian Plane now fresh in our memory we can discuss those sets in more detail andas usual, we begin with a definition.