Schaum's Outline of Theory and Problems of Beginning Calculus

CHAP. 2) COORDINATE SYSTEMS IN A PLANE 132.9 If the points (3, 1) and (- 1,O) are opposite vertices of a rectangle whose sides are parallel to the coordinateaxes, find the other two vertices.2.10 If (2, - l), (5, - l), and (3, 2) are three vertices of a parallelogram, what are the possible locations of thefourth vertex?2.11 Give the coordinates of a point on the line passing through the point (2,4) and parallel to the y-axis.2.12 Find the distance between the points: (a)(2,6) and (7,3); (b)(3, - 1) and (0,2);(c)(43) and (- $, 3).2.13 Determine whether the three given points are vertices of an isosceles triangle or of a right triangle (or ofboth). Find the area of each right triangle.(4 (-1, 21, (3, -21, (7, 6) (b) (4, I), (1, 2), (3, 8) (4 (4, 11, (1, -41, (-4, -1)2.14 Find the value of k such that (3, k) is equidistant from (1,2) and (6, 7).2.15 (a) Are the three points A(l, 0), B(3,4), and C(7,8) collinear (that is, all on the same line)? [Hint: If A, B, Cform a triangle, the sum of two sides, AB + E, must be greater than the third side, AC. If B liesbetween A and C on a line, AB + = x.1(b) Are the three points A( - 5, - 7), B(0, - l), and C( 10, 11) collinear?2.16 Find the mid oints of the line segments with the following endpoints: (a) (1, - 1) and (7, 5); (b)(3, 4) and(190);(4($11 and (593).2.17 Find the point (a, b) such that (3, 5) is the midpoint of the line segment connecting (a, b) and (1,2).2.18 Prove by use of coordinates that the line segment joining the midpoints of two sides of a triangle is one-halfthe length of the third side.