Chapter 2: Geometry Snippets …. Review
1. If the lengths of the three sides of a triangle fit a2 + b2 = c2 , then it is a ____________ triangle.
2. The midpoint of two points is really just the ____________ of the points.
3. The formula y=a(x-h)2+k represents a parabola with a ____________ axis.
4. The formula x=a(y-k)2+h represents a parabola with a ____________ axis.
5. The two elements that determine an equation of a circle are the ____________.
6. The equation the gives the distance between the center and a point on the circle is the ____________.
7. A ____________ is the result when a circle revolves around its center point.
8. For a sphere represented by (x-h)2 + (y-k)2 + (z-l)2 = r2, the radius is r and the center is ____________.
9. If two circles are overlapping, the distance between the centers must be ____________ than the sum of the two radii.
10. If two spheres are not colliding, the distance between their centers must be ____________ than the sum of the two radii.
11. Match the pairs of points with the distance between each pair:
I. 130 A. (75,80) and (45,40)
II. 110.45 B. (36,48) and (18,24)
III. 30 C. (9,18,7) and (15,22,13)
IV. 50 D. (100,50,70) and (20,-20,40)
V. 9.38 E. (20,75) and (140,125)
12. Match the following points to their corresponding midpoints:
I. M(10,10) A. (11,30,19) and (15,6,1)
II. M(75,35) B. (6,9) and (4,3)
III. M(17,8,8) C. (15,13) and (5,7)
IV. M(5,6) D. (75,30) and (75,40)
V. M(18,18,10) E. (21,7,12) and (13,9,4)
13. Match the following terms to their meanings:
I. parabola A. the tip of a symmetric arc
II. vertex B. splits a parabola in half so that each side is a reflection of the other
III. horizontal C. a symmetric arc
IV. axis of symmetry D. the type of axis of symmetry of an up-and-down symmetric arc
V. vertical E. the type of axis of symmetry of a sideways symmetric arc
14. Match each parabola with its corresponding vertex:
II. (1,2) B. x = -2(y-3)2 + 6
III. (2,4) C. y = 3(x-4)2 + 2
IV. (3,6) D. x = 4(y-2)2 + 1
V. (6,3) E. y = 5(x-3)2 + 6
15. Match the following terms to their meanings:
I. radius A. the set of all points at a given distance from a fixed point
II. Pythagorean B. the result when a circle revolves around its center point
III. circle C. the distance of all points from the center of a circle
IV. sphere D. a given fixed point in the middle of a circle
V. center E. the theorem that gives the distance between the center and a point on the circle
16. Match the equation of the circle to its center point:
II. (12,-9) B. (x+12)2 + (y-9)2 = 100
III. (25,30) C. (x-12)2 + (y+9)2 = 64
IV. (17,30) D. (x-11)2 + (y-23)2 = 2500
V. (11,23) E. (x-25)2 + (y-30)2 = 784
17. For a sphere with a center of (10,40,-30), match the following farthest vertices to their corresponding radii:
II. r = 30 B. farthest vertex (0,-20,0)
III. r = 67.823 C. farthest vertex (30,70,30)
IV. r = 70 D. farthest vertex (15,25,35)
V. r = 66.895 E. farthest vertex (11,41,-31)
18. Match the equation of the circle with its correct center and radius:
II. r=30, (-20,30) B. (x-20)2 + (y-50)2 = 100
III. r=60, (-25,-25) C. (x+20)2 + (y-30)2 = 900
IV. r=20, (-80,10) D. (x+25)2 + (y+25)2 = 3600
V. r=50, (-40, 30) E. (x+80)2 + (y-10)2 = 400
19. Match the equations for two spheres with the SQUARE of the distance between their two centers:
I. 7125 A. (x+30)2 + (y+20)2 + (z-10)2 = 900 and x2 + (y+40)2 + (z-50)2 = 1600
II. 6100 B. (x-20)2 + (y-30)2 + (z-10)2 = 100 and (x-50)2 + (y+40)2 + (z-30)2 = 2500
III. 6200 C. (x+15)2 + (y-25)2 + (z-5)2 = 1000 and (x-35)2 + (y-45)2 + (z-25)2 = 400
IV. 1200 D. (x+10)2 + (y-40)2 + (z-20)2 = 4500 and (x-40)2 + (y-50)2 + (z-10)2 = 1600
V. 2700 E. x2 + (y+20)2 + (z-40)2 = 3000 and (x-25)2 + (y-60)2 + (z-30)2 = 6400