Unit 1- The coordinate plane, points, lines, and distance 1.Some terminology: In a right triangle, the legs are the sides adjacent to the right angle. The hypotenuse is the side opposite to the right angle. Given the two points A(3, 7) and B(5, 2) find C so that triangle ABC is a right triangle with the right angle at C. How long are legs? How long is the hypotenuse? 2.The main use of the Pythagorean Theorem is to find distances. Originally (6th century BC), however, it was regarded as a statement about areas. Explain this interpretation. 3.The two- part diagram at the right, which shows two different dissections of the same square, was designed to help prove the Pythagorean Theorem. Provide the missing details. 4.If the hypotenuse of a right triangle is 12 and one of the legs is 4, what is the length of the other leg? What is the simplest form in which you can express your answer? 5.Two different points on the line y = 2 are both exactly 13 units from the same point (7, 14). Draw a picture of this situation, and then find the coordinates of these points. 6.The general notation in geometry is that points are labeled with capital letters and coordinates are defined with lowercase letters. Given the two points and what do the subscripts on x and y represent? If triangle ABC is right triangle with C being the right angle a.Find possible coordinates for point C. b.How could you express the length of the side BC? AC? AB? 7.Give an example of a point that is the same distance from (3, 0) as it is from (7, 0). Find lots of examples. Describe the configuration of all such points. In particular, how does this configuration relate to the two given points? 8.Find two points on the line x=3 that are 5 units away from the point (6,2). 9.Verify that the hexagon formed by A = (0, 0), B = (2, 1), C = (3, 3), D = (2, 5), E = (0(-1, 2) is equilateral. Is it also equiangular10.Draw a 20-by-20 square ABCD. Mark P on AB so that AP = 8, Q on BC so that BQ so that CR = 8, and S on DA so that DS = 5. Find the lengths of the sides of quadrilateral there anything special about this quadrilateral? Explain. 11.The sides of a square have length 10. How long are the diagonal of the square? Keep your answer in simplest radical form. What would your answer be if the side had been 6? A(x1,y1)B(x2,y2)
Unit 1- content adapted from Deerfield Academy
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Unit 1- The coordinate plane, points, lines, and distance