Extra-Review ER7 Analytic Geometry

Length of Line Segment / Midpoint of Line Segment
Point of Division of Line Segment
Distance Point to Line

1.    For each of the figures formed by the given points (in metres), determine the perimeter and area:          a.    A (3, -4)     B (-5, 2)      C (3, 6)                                 b.   D (2, 4)     E (6, 2)     F (2, -6)    G (-2,  -4)

2.   What is the length, in metres of the median KM of triangle JKL given the vertices:                     J (7, 1)      K (-2, -1)        L (1,  5)

3.   Ali's home is at point A (2, 1).  Dimensions are in km.       She wants to go to Restaurant R situated 2/5 of the way from Michelle's home  M  to Danielle's home  D,       on segment MD. The coordinates of the endpoints are: M (-4, -1) and  D (1, 9).       Determine the distance between Ali's home and the Restaurant.

4.    Given points   A (-4, -2)     B (-2, 4)   and   C (1, 3)        a.    Use distances to prove that ABC is a right triangle.        b.    Use slopes to prove that ABC is a right triangle.        c.    What are the coordinates of point P dividing AB in the ratio  3 : 4  from A?        d.    What are the coordinates of point Q dividing AC in the ratio  3 : 4  from A?        e.    What can you say about the relative position of PQ and BC?        f.    Determine the area of triangle ABC 5.    Parallelogram ABCD is given with vertices:   A (0, 0)     B (3, 8)      C (x, y)     D (9, 0)        a.    Determine the coordinates of point C.        b.    What are the coordinates of  P point of intersection of the diagonals AC and BD?        c.    Prove, by calculations, that AC bisects BD.        d.    Calculate the area of parallelogram ABCD.        e.    What is the y-intercept of CD? 6.    Two cars are travelling on parallel streets given, in kilometres, by the equations:         y1 = 2x - 3y + 6 = 0        and        y2 = 2x -3y -3 = 0        Determine how far apart the two streets are. 7.    Point P (-3, -1) divides segment AB in the ratio  2 : 3  and the coordinates of A are (-7, -3)        a.    What are the coordinates of endpoint B?        b.    Determine the coordinates of point R if   RA : AB = 1 : 5.        c.    Determine the coordinates of point M if segment MB measures 5,6 units.        d.    If point T is the x-intercept of segment AB, what is the ratio TA : AB ?        e.    Determine the coordinates of point V dividing AB in the ratio  4 : 1

Answers   1.   a.  Perimeter ABC = 28.94 m               Area of ABC =  40 m2    b.  Perimeter DEFG =  26.82 m             Area of DEFG =   39.96 m2    2.  Length of Median KM =  7.21 m    3.  Distance AR =  4.47 km   4. a.  AC2 = AB2 + BC2    b.   mAB = 3         mBC = - 1/3 c.  P ( -3.14 ,  0.57)       d.  Q ( -1.86 , 0.14)           e.  PQ parallel to BC f.   Area of ABC = 10   5. a.   C (12, 8) b.  P ( 6, 4)            c.  PB = PD = 5 d.   Area = 72 d.  (0, -24)                 6.    The distance between the two streets is 2.5 km   7.   a.   B (3, 2) b.   R (-5, -2) c.   M ( -2,  -0.5) d.   T ( -1, 0) e.   V ( 1, 1)