Lesson 3 Leap Frog Solidify Understanding

Ready

In each problem, there will be a pre-image and several images based on the given pre-image. Determine which of the images are rotations of the given pre-image and which of them are reflections of the pre-image. If an image is the result of a rotation and a reflection, then state both. (Compare all images to the pre-image.)

1.

A horizontally-oriented rectangle with a dot located in the top-right corner.

a.

a vertically-oriented rectangle with a dot located in the top-left corner.

b.

a vertically-oriented rectangle with a dot located in the bottom-right corner.

c.

a horizontally-oriented rectangle with a dot located in the top-left corner.

d.

a vertically-oriented rectangle with a dot located in the top-right corner.

2.

A scalene triangle oriented up with largest angle open towards the right.

a.

A scalene triangle oriented down with largest angle open towards the right.

b.

A scalene triangle oriented left with largest angle open towards the top.

c.

A scalene triangle oriented left with largest angle open towards the bottom.

d.

A scalene triangle oriented left with largest angle open towards the top left.

Set

On each of the coordinate grids there is a labeled point and line. Use the line as a line of reflection to reflect the given point. Label the image of the point as indicated.

(Hint: points reflect along paths perpendicular to the line of reflection. Use perpendicular slope!)

3.

Reflect point over line and label the image .

A coordinate plane with x- and y- axis of 1-unit increments. A line labeled m with y-intercept of 2 and slope of 3. Point A located at (-3,3). x–5–5–5555y–5–5–5555000

4.

Reflect point over line and label the image .

A coordinate plane with x- and y- axis of 1-unit increments. A line labeled k with y-intercept of 1 and slope of -1/2. Point B located at (-5,1). x–5–5–5555y–5–5–5555000

5.

Reflect point over line and label the image .

A coordinate plane with x- and y- axis of 1-unit increments. A line labeled l with y-intercept of -3 and slope of 3/2. Point C located at (3.5,-1). x–5–5–5555y–5–5–5555000

6.

Reflect point over line and label the image .

A coordinate plane with x- and y- axis of 1-unit increments. A line labeled m with y-intercept of 2 and slope of -1/6. Point D located at (4.5,5.5). x–5–5–5555y–5–5–5555000

For each pair of points, and , draw in the line of reflection needed to reflect onto . Then find the equation of the line of reflection.

7.

A coordinate plane with x- and y- axis of 1-unit increments. Point P located at (1,0) and Point P' located at (5,2). x–5–5–5555y–5–5–5555000

8.

A coordinate plane with x- and y- axis of 1-unit increments. Point P located at (-5,0) and Point P' located at (5,-2). x–5–5–5555y–5–5–5555000

Rotate the given figure as described.

9.

Rotate clockwise around .

A coordinate plane with x- and y- axis of 1-unit increments with a left-pointing arrow. The arrow contains the following vertices: H (-9,-1), F (-7,2), D(-7,1), C (-3,1), B (-3,-2), E(-7,-2), G(-7,-3). Point A is separate from the arrow and is located at (-3,-4). x–5–5–5555y–5–5–5555000

10.

Rotate clockwise around .

A coordinate plane with x- and y- axis of 1-unit increments with a triangle stick person facing downward. The stick person contains the following points: (4,3), (5,1), (6.5,-3), (5,-3), (6,-5), (8,-3), (8,1), (9,3). Point A is separate from the arrow and is located at (1,-2). x–10–10–10–5–5–5555101010y–5–5–5555000

Go

For each linear equation, write the slope of a line parallel to the given line.

11.

12.

13.

For each linear equation, write the slope of a line perpendicular to the given line.

14.

15.

16.

Find the slope between each pair of points. Then, using the Pythagorean theorem, find the distance between each pair of points. You may use the graph to help.

17.

a blank 17 by 17 grid

Slope:

Distance:

18.

a blank 17 by 17 grid

Slope:

Distance: