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# Algebra/algebra 2

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

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

(-Ö

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:

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)

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)

Algebra

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