Y ( , ) R ( , ) T ( , ) -2 3 Y’ ( , ) R’ ( , ) T’ ( , ) -1 1.5 2 1 Learning Objective We will reflect1 geometric figures on a coordinate plane. What are we going to do? CFU Standard 7.G.1 Verify experimentally the properties of Transformations2. Our focus today will be REFLECTIONS. 1 create a mirror image (synonym) 2 making changes to original Vocabulary Activate Prior Knowledge We have worked with a few different types of Transformations. We first looked at Dilations. Dilations change the size through enlargement or reduction, but do not alter the shape. All sides maintain proportional relationships. DILATION OF 0.5 Y’ Y ( , ) R ( , ) T ( , ) -2 3 Y’ ( , ) R’ ( , ) T’ ( , ) -1 1.5 R’ 2 1 1 0.5 T’ -1 -2 -0.5 -1 Because the dilation is less than 1, our new image will be smaller than the original, in this case ½ the size of the original. How do DILATIONS change the original figure? What operations are used in dilations? CFU 2

+5 (+4 ) RIGHT +4 (+5 ) UP y-axis x-axis (2, 3) x and y Activate Prior Knowledge Ordered Pair (2, 3) x and y The coordinate plane is a flat surface made by the intersection of two perpendicular3 number lines. An ordered pair describes4 the location of a point on the coordinate plane using x- and y-coordinates. Translating5 Ordered Pairs on the Coordinate Plane How do you translate a geometric figure? In your own words, what does it mean to translate an ordered pair? “Translating an ordered pair means ______________.” CFU y-axis – the vertical number line. Locate the point (4,4). In order to move from the (4,4) to Point T’s location, how far does the point need to move horizontally? How far does it move vertically? 2 10 4 5 6 7 8 9 3 1 T +5 3 crossing at a 90 degree angle 4 shows (synonym) 5 moving in one or more directions (synonym) Vocabulary (+4 ) RIGHT (4, 4) 4 4 +4 (+5 ) UP x-axis – the horizontal number line. 1 2 3 4 5 6 7 8 9 10 The origin is where the x-axis and y-axis intersect.

Concept Development Ordered Pair (2, 3) x and y Translating Ordered Pairs on the Coordinate Plane X moves left (if negative) or right (if positive) Y moves down (if negative) or up (if positive) How do you translate a geometric figure? In your own words, how do you determine which direction to move on x axis? On y axis? CFU (-6) = LEFT (+2) = UP

Translation: Move 3 units to left, 4 units down Concept Development Ordered Pair (2, 3) x and y Translating Ordered Pairs on the Coordinate Plane X moves left (if negative) or right (if positive) Y moves down (if negative) or up (if positive) Translation: Move 3 units to left, 4 units down How do you translate a geometric figure? In your own words, why must you also label points with letters? CFU D’ J’ Z’

A Reflection should be equal in distance from the line of reflection. Concept Development Reflections6 take an image and create a mirror-like image across a line of reflection. A preimage is the original shape or figure. Image refers to the new figure or shape that you will create. A Reflection should be equal in distance from the line of reflection. How can you use a grid (graph paper) to create a reflection? CFU 6 mirror image of original (synonym) Vocabulary

Reflections on the Coordinate Plane Concept Development (Continued) The line of reflection is often either the x-axis or the y-axis. Preimage points (ordered pairs) can be measured from the line of reflection. The new image should be the same distance away. Look at Point A. Calculate the number of units Point A is from the Y axis. How can you use this to determine the position of the new point? How does this work for Point B? How does this work for point C? CFU Reflections on the Coordinate Plane

A Reflection should be equal in distance from the line of reflection. Guided Practice Reflections6 take an image and create a mirror-like image across a line of reflection. A preimage is the original shape or figure. Image refers to the new figure or shape that you will create. A Reflection should be equal in distance from the line of reflection. How can you use a grid (graph paper) to create a reflection? CFU 6 mirror image of original (synonym) Vocabulary

Plot your new points and label accordingly. Sketch your new figure. Skill Development / Guided Practice Determine where the line of reflection is. The line of reflection will be horizontal (if line is the x-axis) and it will be vertical (if line is the y-axis) Plot your new points and label accordingly. Sketch your new figure.

Directions: REFLECT EACH FIGURE ACROSS THE Y-AXIS. Guided Practice Determine where the line of reflection is. The line of reflection will be horizontal (if line is the x-axis) and it will be vertical (if line is the y-axis) Plot your new points and label accordingly. Sketch your new figure. Directions: REFLECT EACH FIGURE ACROSS THE Y-AXIS.

Directions: REFLECT EACH FIGURE ACROSS THE X-AXIS. Guided Practice Determine where the line of reflection is. The line of reflection will be horizontal (if line is the x-axis) and it will be vertical (if line is the y-axis) Plot your new points and label accordingly. Sketch your new figure. Directions: REFLECT EACH FIGURE ACROSS THE X-AXIS.

Skill Closure Determine where the line of reflection is. Is the picture below showing reflection across the x-axis or the y-axis? How can we determine if we have properly reflected the figure preimage (black figure)? A reflection over a line is a transformation in which each point of the original figure (pre-image) has an image that is the same distance from the line of reflection as the original point but is on the opposite side of the line.  Remember that a reflection is a flip.  In a reflection, the figure does not change size.  How is a reflection similar to a translation? How is a reflection different from a dilation? CFU