Lesson 2 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.

b.

c.

d.

2.

a.

b.

c.

d.

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 $A$ over line $m$ and label the image $A^{'}$ .

4.

Reflect point $B$ over line $k$ and label the image $B^{'}$ .

5.

Reflect point $C$ over line $l$ and label the image $C^{'}$ .

6.

Reflect point $D$ over line $m$ and label the image $D^{'}$ .

For each pair of points, $P$ and $P^{'}$ , draw in the line of reflection needed to reflect $P$ onto $P^{'}$ . Then find the equation of the line of reflection.

7.

8.

Rotate the given figure as described.

9.

Rotate $90 °$ clockwise around $(- 3, - 4)$ .

10.

Rotate $180 °$ clockwise around $(1, - 2)$ .

Go

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

11.

$y = - 3 x + 5$

12.

$y = 7 x - 3$

13.

$3 x - 2 y = 8$

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

14.

$y = - \frac{2}{7} x + 5$

15.

$y = \frac{1}{5} x - 4$

16.

$3 x + 5 y = - 15$

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.

$(- 2, - 3) (1, 1)$

Slope:

Distance:

18.

$(- 7, 5) (- 2, - 7)$

Slope:

Distance: