1. Plot and label the points
A(-3,-7),B(1.3,-2),C(π,√10),D(0, 8),E(-5.5, 0),F(-8, 4),G(9.2,-7.8) andH(7, 5) in the Cartesian Coordinate Plane given below.xy-9-8-7-6-5-4-3-2-1123456789-9-8-7-6-5-4-3-2-11234567892. For each point given in Exercise1above• 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.In Exercises3-10, find the distancedbetween the points and the midpointMof the line segment whichconnects them.3. (1, 2), (-3, 5)4. (3,-10), (-1, 2)
1258Algebra Review11. Let’s assume that we are standing at the origin and the positivey-axis points due North while thepositivex-axis points due East. Our Sasquatch-o-meter tells us that Sasquatch is 3 miles West and4 miles South of our current position. What are the coordinates of his position? How far away is hefrom us? If he runs 7 miles due East what would his new position be?12. Verify the Distance FormulaA.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.)13. Verify the Midpoint Formula by showing the distance betweenP(x1,y1) andMand the distancebetweenMandQ(x2,y2) are both half of the distance betweenPandQ.14. Show that the pointsA,BandCbelow are the vertices of a right triangle.BCBC15. Find a point
D(x,y) such that the pointsA(-3, 1).B(4, 0),C(0,-3) andDare the corners of asquare. Justify your answer.16. Suppose the distance betweenC(h,k) andP(x,y) isr. Use the distance formula to show(x-h)2+ (y-k)2=r2We will see this formula (and its cousins) in Chapter7.17. LetP(x,y) be a point in the plane and letQbe the result of reflectingPabout thex-axis,y-axis, ororigin. Show the distance from the origin toPis the same as the distance from the origin toQ.18. LetO(0, 0) (that is,Ois the origin),P(-2, 1),Q(-4, 2), andR(6,-3).(a) Find the distance fromOtoPand fromOtoQ. What do you notice?(b) Find the distance fromOtoPand fromOtoR. What do you notice?