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Algebra/algebra 2

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Question
1.

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






3

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:



(

2

, 1)

and


(-

2

, 0)











(0, 0.5)



(0.5, 0)








(

1

, -2)







(

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:














x

+

y





x + y










x2 + y2









x2

+

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 = 3

3







C(-5, 2); r = 2

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
1. d=7.28, 2. d=2.5, 3. d=3.47, 4. d=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 right triangle, 16. 9, 17. y=2x+2, 18. y=2.5x+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. C(0,0),r=9, 23. C(-5,2),r=3(3^1/2)
24. C(0,2.5),r=1.5, 25. C(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)

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