1. Two masts AB and DC of a ship, and the cable rigging securing them are shown on the graph.

    A(4, 2) B (4, 7) C(15, 11) D(15, 2)
 

a. What is the distance between the two masts? b. What is the length of the cable joining B to C? c. A flag is placed at a point P that divides BC in the      ratio 7:3 starting from B. What is the length of BP? d. What is the slope of cable BC? e. If CE is perpendicular to BC. What is the slope of CE?

 
 

2. Points A(-80, -40), B(-20, 50) and C(124, -46) represent the position of three summer cottages on
    a Cartesian grid, scaled in metres.
 

a. 1. What is the equation for trail AB?     2. What is the equation for trail AC? b. What is the equation of power line DE going through      D(-40, 60) and parallel to AB? c. From cottage B a straight road BH perpendicular to AC     is built. What is the equation of BH?

 
 

3. A triangular pond ABC is represented in the graph shown, scaled in metres.

    A(-3, -4)         B(6, 5)         C (12, 1)

    A water pump is installed at point P ( 5, 1)
 
 

a. What is the distance between the pump P and sides:      1. AB?             2. AC?           3. BC?     b. What is the area of the pond?

 
 
 
 

DISTANCE. MIDPOINT. POINT OF DIVISION

PART B

For each of the following questions, select the most correct answer.
 
 

1. What is the distance between A(-8,9) and B(12,2)?
    a. V65         b. V137         c. V351         d. V449
 

2. The straight line 3x + 4y = 12 intersects the x-axis and the y-axis at 2 points. What is the
    distance between the 2 points?
    a. 5/12         b. 7/12         c. 5             d. 7
 
 
 

3. What are the coordinates of a point R situated 3/4 of the way from P(-2,1) to Q(5,-1)?
    a. (9/4, 0)     b. (1, 1/7)     c. (18/5, -4/5)     d. (13/4, 1/2)
 
 
 

4. Find the distance between the points A(3,-2) and B(5,-3)
    a. V5             b. 5             c. V89                   d. 89
 
 
 

5. If M(1, n) is the midpoint of segment AB and A = (V3, 7) find the coordinates of B

        a. (1 + V3, n + 7)
        b. (2 - V3, 2n - 7)
        c. (2V3 -1, 14 - n)
        d. (1 - V3, n - 7)
 
 
 

6. What is the distance between point A(-4, 6) and point B(2, 8)
    a. 2V2             b. 4 V2             c. 2V10             d. 10V2
 
 
 
 

7. Find the coordinates of the midpoint of segment CD connecting points
                                C(a + 1, b - 1) and D(-1, b + 1)

    a. (2a + 1, -1)         b. (2a + 1, -2)         c. (1, 2b)         d. (1/2, b)
 
 
 
 

8. If (a, b) is the midpoint of segment OP, in which O is the origin, find the coordinates of the
    other endpoint P

    a. (-a, -b)         b. (2a, 2b)         c. (a, b)         d. (a + b, 0)
 
 
 

9. Find the distance between points R(-3,7) and G(2,-5)

    a. 5                 b. V145             c. 13                d. V29
 
 
 

10. What is the distance between points A(-6, 3) and B(-2,-5)

    a. 2V5             b. 2V17             c. 4V5             d. 8V2
 
 
 
 
 
 
 

ANALYTIC GEOMETRY ANSWERS:

PART A
 

1.  a.  AD = 11 m           b.  BC = 11,70 m         c.  BP = 8,2 m
    d.  mBC = 0,36         e.  mEC = 2,78
 

2.  a. AB   y = 0,9 x + 32         AC   y = - 0,03 x - 42,4
     b. y = 0,9 x +96
     c. y = 33,3 x - 616,3
 

3.  a. 1.  2,12 m             2.  0,32 m                 3.  1,11 m
     b.  Area = 30 m²
 

PART B

    1d         2c         3d         4a         5b

    6c         7d         8b         9c         10c