1 / 11

Lesson 19

Lesson 19. Reflections, Rotations, and Translations on the Coordinate Plane. Transformations. A transformation can be used to change a figures position.

yagil
Download Presentation

Lesson 19

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Lesson 19 Reflections, Rotations, and Translations on the Coordinate Plane

  2. Transformations • A transformation can be used to change a figures position. • The first type we will discuss is a reflection. This is a flip of a figure across a point of an axis. The result will look like a mirror image of the pre-image. (the pre-image is the figure you start off with, before you perform a transformation).

  3. Of course, there are rules • If a point is reflected over the x –axis, every point (x,y) becomes (x,-y). • If a point is reflected over the y-axis, every point (x,y) becomes (-x, y).

  4. Example 1 • Reflect Triangle ABC across the x-axis. • Pt A (2,2); pt B (4,6); pt c (8,3) • New points (2, -2) (4, -6) (8,-3)

  5. Rotation • The second type of transformation is rotation. A rotation is a turn of a figure around a point. • 90° counter clockwise 180 °

  6. Example 2 • Rotate Triangle PQR 180 clockwise around point Q. { pt P (1,1); pt Q (4,1); pt R (4,3)} • Since we are rotating around pt Q, it stays in the same spot. • What happens to pt P? • After 180° rotation, point P will be at (7,1) • What about pt R? • Point R will be at (4, -1)

  7. What about a rotation around the origin? • What if we were asked to rotate an object around the origin (0,0)? There is a short cut we can use!! • If you are asked to rotate 90 clockwise: your point (x,y) becomes (y,-x). • If you are asked to rotate 90counter clockwise: your point (x,y) becomes (-y, x) • If you are asked to rotate 180clockwise OR counter clockwise, point (x,y) becomes (-x,-y)

  8. Example 2a • Rotate Triangle PQR 90 clockwise around the origin. { pt P (1,1); pt Q (4,1); pt R (4,3)} • Since we are rotating around the origin, the shape is going to move from ne quadrant to the next. • Point P will become (1,-1) • Point Q will become (1,-4) • Point R will become (3, -4) R Q P P R Q

  9. Translation • A translation is a slide of a figure to another location on a coordinate plane. • When a figure it translated, your figure is moved along the x axis (right and left) and/or along the y axis (up and down). • Every point (x,y) becomes (x+a, y+b). • A is adding your right or left movement to x. • B is adding your up or down movement to y.

  10. Example 3 • Triangle HJK is translated 6 units to the left. Identify its coordinates. • H (2,2); K (6,3); J (4,4) • What would 6 units left look like with numbers? Moving left will change x. • H (2-6,2); K (6-6,3); J (4-6,4) • The new coordinates are: H1(-4,2); K1 (0,3); J1 (-2,4)

  11. Let’s try some practice problems • Take out you Coach book and lets put what we learned to practice. • Complete numbers 1-6 on pages 122-123. We will complete the open ended together so we can review the SEA method. • Remember, if you are stuck, consult a partner.

More Related