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