Expert: Richard J. Raridon - 12/23/2011

Question
Find the distance between the pair of points:
(9, 1) and (2, -1)

      d = 9.9         d = 7.28
      d = 7          d = 21.17
2.      Find the distance between the pair of points:
(0.5,-1) and (-1,1)

      d = 3.54          d = 3.55
      d = 2.5         d = 0.5
3.      Find the distance between the pair of points:
(3.45, 0.32) and (1.45, 3.15)

      d = 3.47          d = 2.45
      d = 6.93          d = 2.83
4.      Find the distance between the pair of points:
(-a,b) and (2a,4b)

      ab
3Ö      a2 + b2
      3ab          a2 + b2
5.      Find the midpoint of the line segment joining the points:
(13,6) and (0,6)

      (6.5,0)         (13,12)
      (6,6.5)         (6.5,6)
6.      Find the midpoint of the segment joining the points:
(0.5,-1) and (-1,1)

      (-2, 0)         (-0.25, 0)
      (-0.5, 0)          (0.25, 0)
7.      Find the midpoint of the segment joining the two points:
(3.45, 0.32) and (1.45, 3.15)

      (2.45, 1.735)          (4.90, 3.46)
      (1.735, 0.87)          (3.46, 4.90)
8.      Find the midpoint of the line segment joining the two points:
(-a, b) and (2a, 4b)

      (1.5a, 2.5b)          (0.5a, 1.5b)
      (0.5a, 2.5b)          (2a, 0.4b)
9.      Find the coordinates of Q given that M is the midpoint of line segment PQ:
P(-4, 3) and M(0, 0)

      (0, 3)          (1, -4)
      (0, 0)          (4, -3)
10.     Find the coordinates of Q given that M is the midpoint of line segment PQ:
P(6, -2) and M(0, 5)

      (4, 8)          (6, -12)
      (-6, 12)          (12, -6)
11.     Find the coordinates of Q given that M is the midpoint of line segment PQ:
P(0, 0) and M(h, k)

      (2h, 2k)          (h, k)
      (-2k, -2h)          (2h, k)
12.     Find the midpoint of the segment joining the two points:
(Ö      2       , 1)
and
(-Ö     2       , 0)
      (0, 0.5)          (0.5, 0)

(Ö      1       , -2)

(Ö      2       , -1)
13.     Find the midpoint of the segment joining the two points:
(0.5, -1) and (-1, 1)

      (-0.25, 0)          (0, -0.25)
      (0.25, 0)          (0, 0.25)
14.     For the given vertices what type of triangle is formed:
Vertices:  A(4, -5), B(-2, -8), C(-8, 4)

      Right          Obtuse
      Isosceles          Equilateral
15.     For the given vertices what type of triangle is formed:
Vertices:  A(2, -3), B(2, 3), C(5, 0)

      Isoceles right triangle         Isosceles
      Equilateral          Scalene right triangle
16.     What is the area of the triangle formed with the given vertices:
Vertices: A(2,-3), B(2,3), C(5,0)

      9          18
      81          27
17.     Find an equation of the perpendicular bisector of line segment AB:
A(2, 1), B(-2, 3)

      y = 2x - 2          y = 2x + 2
      y = 4x - 2          y = 4x + 2
18.     Find an equation of the perpendicular bisector of line segment AB:
A(-9, -3), B(1, -7)

      y = 2x + 5          y = 2.5x + 15
      y = 2.5x + 5          y = 0.4x + 15
19.     Find the distance from any point (x,y) to the origin:

Ö       x        + Ö    y
      x + y

Ö       x2 + y2

Ö       x2       + Ö    y2
20.     Find an equation of the circle with the center and radius:
(-3, 1); r = 5

      (x - 3)2 + (y + 1)2 = 25          (x + 3)2 + (y - 1)2 = 25
      (x - 3)2 + (y + 1)2 = 5         (x + 3)2 + (y + 1)2 = 5
21.     Find an equation of the circle with the center and radius:
(-5,3); r = 0.167

      (x + 5)2 + (y - 3)2 = 0.028          (x + 5)2 + (y - 3)2 = 0.167
      (x - 5)2 + (y + 3)2 = 0.167          (x - 5)2 + (y + 3)2 = 0.028
22.     Find the center and radius of a circle with equation:
x2 + y2 - 81 = 0

      C(1, 1); r = 3          C(0, 0); r = 3
      C(1, 1); r = 9          C(0, 0); r = 9
23.     Find the center and radius of a circle with equation:
x2 + y2 + 10x - 4y + 2 = 0


C(-5, 2); r = 3Ö        3

C(-5, 2); r = 2Ö        3
      C(5, -2); r = 9         C(5, -2); r = 3
24.     Find the center and radius of a circle with equation:
x2 + y2 - 5y + 4 = 0

      C(0, 2.5); r = 1.5          C(0, -2.5); r = 2.25
      C(0, 2.5); r = 2.25          C(0, -2.5); r = 1.5
25.     Find the center and radius of a circle with equation:
4x2 - 16x + 4y2 - 24y + 36 = 0

      C(2, 3); r = 2          C(2, 3); r = 3
      C(3, 2); r = 2          C(3, 2); r = 3
26.     Find the equation of a circle:
center (-2, 0); passes through (2, 0)

      (x + 2)2 + y2 = 16          (x - 2)2 + y2 = 4
      (x + 2)2 + (y + 0)2 = 4         (x - 2)2 + y2 = 16
27.     Find the equation of the circle:
center on line x + y = 4; tangent to both first quadrant coordinate axes

      (x + 2)2 + (y + 2)2 = 2         (x - 2)2 + (y - 2)2 = 2
      (x + 2)2 + (y + 2)2 = 4         (x - 2)2 + (y - 2)2 = 4
28.     If the directrix of a parabola is:
D: y = 2 and the vertex is V(2, 4), what is the focus?

      F(-2, 6)          F(4, 0)
      F(0, 4)         F(2, 6)
29.     If the focus of a parabola is F(-3, -1) and vertex is V(1, -1), what is the directrix?
      D: x = 5          D: x = -1
      D: x = -3          D: x = -5
30.     If the directrix of a parabola is D: x = -7 and the vertex is V(1, 3), what is the focus?
      (-10, 5)          (9, 3)
      (3, 5)          (-3, 10)

Answer
It would have been quicker to answer if you had labeled your answers a),b),c),d)
1. d=7.28
2. d = 2.5
3. d = 3.47
4. 3(a^2+b^2)^1/2
5. 6.5,0
6. -0.25,0
7. 2.45,1.735
8. 0.5a,2.5b
9. 4,-3
10. -6,12
11. 2h,2k
12. 0,0.5
13. -0.25,0
14. right
15. isoceles
16. 9
17. y=2x+2
18. y=2.5+5
19. (x^2+y^2)^1/2
20. (x+3)^2+(y-1)^2 = 25
21. (x+5)^2+(y-3)^2 = 0.028
22. (0,0);r=9
23. (-5,2);r=3(3)^1/2
24. (0,2.5);r=1.5
25. (2,3);r=2
26. (x+2)^2+y^2 = 16
27. (x-2)^2+(y-2)^2 = 4
28. (2,6)
29. x=-5
30. (9,3)