Transformations
Circles
Completing the Square
Parabolas & Lines
Miscellaneous
100

Classify each type of transformation (translation, reflection, or dilation):

a.  (x, y) -> (x+1, y-1)

b.  (x, y) -> (2x, 2y)

c.   (x, y) -> (-x, y)


a. Translation

b. Dilation

C. Reflection 

100

A circle has center (9, -6) and radius 7 units. Write an equation that represents the circle.

(x-9)^2+(y+6)^2=7^2

100

What is the first step to completing the square to find the radius and center of the circle given by the equation  x^2+y^2+8x-6y+21=0 ?

Rearrange the equation so that like terms are together and the constant (21) is on the right side 

x^2+8x+y^2-6y=-21

100

The parabola has a focus at (6, 2). Its directrix is the line y=1. Write an equation to represent the parabola.

(x-6)^2+(y-2)^2=(y-1)^2

100

Use the Pythagorean Theorem to find the length of side AD of the square.


3^2+4^2=c^2

9+16=c^2

25=c^2

c=sqrt25=5

200

Describe the transformation used to take figure F to figure G

Translation 6 units down and 2 units left

200

Describe the process to test if a point is on a circle.

Plug the x and y values of the point in for x and y in the equation. If you end up with the same number on both sides of the equation, the point is on the circle. 

200

Find the missing numbers to complete the square:  x^2+8x+[ ]+y^2-6y+[ ] =-21+[ ]+[ ] 

x^2+8x+16+y^2-6y+9 =-21+16+9

200

The point (9, 6) is on the parabola. Find the distance between this point and the focus. 


5 (same as the distance to the directrix)

200

What needs to be true for a quadrilateral to be a square?

All sides must be equal and all angles must be 90 degrees
300

What types of transformations result in figures that are congruent to the original?

Rigid Transformations (translations, reflections, and rotations)

300

Use your equation from #1 to identify if point (9, 1) lies on the circle.

(9-9)^2+(1+6)^2=7^2

0+7^2=7^2

49=49

300

What should you do after finding your missing numbers?

Add up the numbers on the right side

OR

Rewrite the equation using squared binomials

300

Write an equation for a line with slope  3/7  passing through point (7, -1).

y+1=3/7(x-7)

300

How do you find the perimeter of a square?

Add up all the side lengths

400

What types of transformations result in figures that are similar to the original?

Dilations

400

Find the center and radius of the circle:

(x-6)^2+(y+4)^2=36

Center: (6, -4) Radius: 6

400

Rewrite the equation  x^2+8x+16+y^2-6y+9=4  using squared binomials.

(x+4)^2+(y-3)^2=2^2

400

Write an equation for a line that passes through point

 (6, 2) that is parallel to 

 y-3=2(x+1) .

y-2=2(x-6)

400

How do you find the area of a square?

length x width

OR

side^2

500

Describe how you would perform the transformation  (x, y)-> (x-4, y+3) 

Move each point on the shape 4 units to the left and 3 units up. Connect these new dots to form the new shape. 

500

Rewrite  x^2+8x+16+y^2-14x+49=81 using squared binomials. 

(x+4)^2+(y-7)^2=9^2

500

What is the radius and center of the equation from #4?

Center: (-4, 3) Radius: 2

500

Line p is represented by the equation  y-1=1/2(x+2) . Select all equations that represent lines perpendicular to line p. 

A.  y=-1/2x+4 

B.  y=2/1x+4 

C.  y=-2/1x+4 

D.  y=-4/2x+4 

C, D

500

How would you find the slope of a line that passes through points (3, 6) and (7, 10)?

(rise)/(run)=(y_2 -y_1)/(x_2-x_1)=(10-6)/(7-3)=4/4=1