8th Grade TAKS Review 2008 Objective 3 Day 1

Dilations A Dilation is the enlargement or reduction of a figure Every Dilation must have a Scale Factor A Scale Factor < 1 (less than 1) indicates a reduction A Scale Factor > 1 (greater than 1) indicates an enlargement On the coordinate grid, simply multiply each point by the scale factor Obj. 3: 8.6A

Dilations, cont… Example: ΔTUV has vertices T(-2,3), U(2,2), and V(-2,-3). ΔTUV is dilated by a scale factor of 2 and has the origin as the center of dilation. What are the coordinates of U’? (2, 2) times 2 = (4, 4) (-4, 6) (4, 4) (-4, -6) (-2, -3) Obj. 3: 8.6A

Dilations, cont… Identifying the scale factor when you don’t have a coordinate grid… Find a pair of corresponding sides that you know Place the sides into a ratio (fraction) KEEP THE ORDER OF THE SHAPES IN MIND! Obj. 3: 8.6A

Dilations, cont… Example: ΔABC ~ ΔMNO is shown below. Which scale factor was used to transform ΔMNO to ΔABC? ΔMNO ΔABC Because our triangle became larger (enlargement) we choose the answer >1 : 5 3.33 : A B C M N O 1 : 5 4.5 3 3 15 15 22 Obj. 3: 8.6A

Transformations Four types of Transformations Translation (slide) Reflection (flip over) Obj. 3: 8.6AB

Translations After you have identified the problems as a translation Determine the right/left shift and the up/down shift Repeat the process for each point The new shape should look identical to the old one, just in a different place Obj. 3: 8.6B

Translations, cont… Example: ΔDEF is translated 3 units to the right and 3 units down. Which coordinate pair best represents F’? (4, 2) (-1, -3) (3, -6) (0, -3) D’ F’ Obj. 3: 8.6B

Reflections After you have identified the problem as a reflection Determine the line that the image will reflect over (the x or y-axis) Reflect each point over the indicated line Obj. 3: 8.6B

Reflections, cont… Example: ΔMNO is shown on the coordinate plane below. What will be the coordinates of N’ if ΔMNO is reflected across the x-axis? (-4, -3) (-1, -5) (3, -2) (1, 5) (3, -2) (-4, -3) (-1, -5) Obj. 3: 8.6B

Views of 3-D Solids You must be able to imagine a 3-D solid from every angle Left Front Left Top Right 1 3 2 Right Front Obj. 3: 8.7A

Views of 3-D Solids, cont… Example: Match the three views of this solid to its 3-dimensional sketch. Front Right Top A. B. C. D. Obj. 3: 8.7A

Vocabulary Transformation – a change made to a shape Dilation – to make a shape bigger or smaller Scale Factor – the number of times larger a shape becomes Enlargement – to make a shape larger Reduction – to make a shape smaller Translation – to slide a shape Reflection – to flip a shape over a line 3-dimensional – figure with length, width, and height