Circles
What is the radius of a circle?
The distance from the center to the edge.
What is the rule for a 90 degree CCW rotation?
(x,y)--> (-y,x)
Write the rule for translating 5 to the left and 2 up.
(x,y)-->(x-5,y+2)
Describe how we could combine two translations.
Find the net horizontal and vertical change. Add up the change in x and in y.
What is the slope of the line that goes through the points (3,2) and (-1,5)?
- 3/4
If a circle has an equation
(x-2)2 + (y+2)2 = 4,
where is the center of that circle?
(2,-2)
What type of transformation is represented by the rule
(x,y)-->(3x,3y) ? How do you know?
This is a dilation. We know this because x and y are both multiplied by the same value. Dilations are the only transformations that us multiplication!
The rule (x,y)-->(y,x) describes which reflection?
Across the line y = x.
Write one rule to represent the following composition of transformations.
1. Dilate by a scale factor of 12
2. Dilate by a scale factor of 1/3
(x,y)-->(4x,4y)
Calculate the distance between the points (1,-1) and (4,5).
Sqrt of 45 ~ 6.7
What is the equation of a circle with a center at (3,-4) and a radius of 5?
(x-3)2 + (y+4)2 = 25
The rule (x,y)-->(y,-x) can represent multiple rotations, give at least two of these possibilities.
270 CCW Rotation
90 CW Rotation
The rule for reflecting across the x-axis is (x,y)--> (x,-y). Explain why this makes sense.
When we reflect over the x-axis, the shape or points will move straight across the axis at an equal distance. This means the x-value will stay the same and the y-value will change its sign.
Write one rule to represent the following composition of transformations.
1. 180 degree rotation
2. Translation left 1 and down 3
(x,y)-->(-x-1,-y-3)
Give any two slopes that would represent perpendicular lines.
Answers may vary. Slopes must be opposite reciprocals and multiply to -1
What is the equation of a circle with a radius of 1 and a center at (-2,1)?
(x+2)2 + (y-1)2= 1
If a shape is dilated by a scale factor of 3, the area of its image will be ____________ times larger than the original area.
9
Reflect the point (5,-2) across the line y = -x
(2,-5)
Write one rule to represent the following composition of transformations.
1. Rotation 90 degrees CW
2. Reflection across the line y=x
(x,y)-->(-x,y)
How can you use slopes to prove that a shape is a rectangle?
You can show that opposite sites have the same slope (parallel) AND that consecutive sides are perpendicular (slopes are opposite reciprocals).
What is the center and radius of the circle with equation: (x-5)2 + (y-2)2 = 4 ?
Center is at (5,2) with a radius of 2
Triangle ABC has a perimeter of 14 and an area of 32.
If triangle ABC is dilated by a scale factor of 0.5, what is the perimeter and area of the image?
Perimeter = 7
Area = 8
Reflecting across the x-axis and then the y-axis results in what single transformation?
A 180 degree rotation.
Write one rule to represent the following composition of transformations.
1. Translation 3 right and 1 down
2. Dilation with magnitude 0.5
(x,y)-->(0.5x+1.5,0.5y-0.5)
If two lines are parallel, their slopes are_____________?
The same. Equal.