Mar 04, 2015 how to dilate reduce and enlarge using coordinate points on the coordinate plane. Find the coordinates of the image without graphing. Grade 8 mathematics grade 8accelerated mathematics unit 6. You can multiply the coordinates of the point by the scale factor r to find the coordinates of the new image point. Use coordinates to describe the transformations and give the scale factor you used. In lesson 5, we found the location of a dilated point by using the knowledge of dilation and scale factor, as well as the lines of the coordinate plane to ensure equal angles, to find the coordinates of the dilated point. Unit 5 the tools of coordinate geometry emathinstruction. Watch in 360 the inside of a nuclear reactor from the size of an atom with virtual reality duration. Dilations in the coordinate plane pdf by common core. Dilations practice worksheet teachers pay teachers. Section 76 dilations and similarity in the coordinate plane.
Imagine a ray that starts at a fixed point and passes through each point on a figure. Figure 1 so that it lies entirely in quadrant iii on the coordinate plane. Describe the transformation in as much detail as possible. You may perform the transformations in any order that you choose. Reading diagrams in this chapter, for all of the dilations in the coordinate plane, the center of dilation is the origin unless otherwise noted. Drawing triangles in a coordinate plane use what you learned about dilations to complete exercises 46 on page 87. For example, we were given the point 5,2 and told the scale factor of dilation was 2.
The triangle is dilated from the origin by scale factor. Dilations have a multiplicative effect on the coordinates of a point in the plane. Improve your math knowledge with free questions in dilations. Dilations in the coordinate plane, with the origin as the center of dilation, can be done by multiplying the coordinates by the scale factor. In the coordinate plane, when the center of dilation is the origin, to effect a dilation of scale factor k, you multiply each coordinate of the points of the original figure by k. Classwork example 1 7 minutes students learn the multiplicative effect of scale factor on a point. Students describe the effect of dilations on twodimensional figures using coordinates lesson 6. This allows us to specify the exact coordinates of the preimage, image, point of rotation, and line of reflection. On a coordinate plane, the center of dilation is always the origin. Students continue looking at twodimensional figures on the coordinate plane, concentrating on the coordinates of the resulting figure after transformations, including dilations learned in grade 7. On this page you can read or download dilations gina wilson 2015 in pdf format. The notation ofa dilation in the coordinate plane is given by do, y kr, o.
Determine whether the dilation from figure a to figure b is a the values of the variables. For a dilation with scale factor k, you can find the image of a point by multiplying each. Coordinate notation x, y x a, y b leftright updown example 3. Note that this effect holds when the center of dilation is the origin. The center of dilation is the origin and the scale factor is k 4, then 3, 2 12, 8. Describe the effect of dilations, translations, rotations, and reflections on twodimensional figures using coordinates. C compare the coordinates, side lengths, and angle measures of abc. How do you think the rule would change if the scale factor was 3. Other results for dilations worksheet answer key kuta. Dilations dilations are transformations that change the. Objects in the coordinate plane can also be dilated.
Coordinate rule for dilations if px, y is the preimage of a point, then its image after a dilation centered at the origin 0, 0 with scale factor k is the point p. Abc after a dilation with center at the origin o and a. The segment will be dilated with a scale factor of. Dilations practice state whether a dilation using the scale factor k results in a reduction or an enlargement of the original figure. Draw triangle bog with vertices b3, 1, o7, 1, and g5, 6. Use either the x or y coordinate to find the scale factor.
Coordinate plane lets label the axes, quadrants, and signs on the following grid. Grade 8 mathematics grade 8accelerated mathematics unit. Use dynamic geometry software to draw any triangle and label it abc. A dilation is an enlargement or reduction of an object by a scale factor and with a center of dilation.
Then draw a dilation of the figure with the given vertices using the given scale factor k. Students know an informal proof of why dilations are degreepreserving transformations and map segments to segments, lines to lines, and rays to rays. Graphing and describing dilations 11 p a g e 3 4 the table below shows the coordinates of triangle rst and the coordinates of r in triangle rst. A scale factor describes how much the figure is enlarged or reduced. The distance from the center of dilation to the vertex of. Dilate the figure below by a scale factor of 3 from the origin 0,0. Dilate abc using a scale factor of 2 and a center of dilation at the origin to form a.
Dilations on the coordinate plane date when dilating a figure on the coordinate plane, we focus on the coordinates. Symbols x, y rx, o dilations in the coordinate plane words a dilation with a scale factor of k will be. State the quadrant or axis that each point lies in. Make a chart of the preimage coordinates, mapping and compute the new coordinate values, and graph the new image. When the center of dilation in the coordinate plane is the origin, each coordinate of the preimage is multiplied by the scale factor k to find the coordinates of the image. Part a what are the coordinates of point s and point t. It includes questions that ask students to dilate a point in different ways enlargements and reductions using who. The image will be proportionally larger or smaller than the preimage. Jan 28, 2018 watch in 360 the inside of a nuclear reactor from the size of an atom with virtual reality duration. Draw a picture of the new figure at each step and explain the procedures you followed to get the new figure. Dilate the following figure using a scale factor of 2.
Dilations on the coordinate plane student outcomes students describe the effect of dilations on twodimensional figures using coordinates. Students describe the effect of dilations on twodimensional figures using coordinates. Remember that a capital letter, such as, represents the pre. If you dont see any interesting for you, use our search form on bottom v. Describe the effects of dilations, translations, rotations, and re. Write a ratio of the xor ycoordinate of one vertex of the dilation to the xor ycoordinate of the corresponding vertex of the original figure. The scale factor is multiplied by each coordinate in the ordered pair. How to dilate reduce and enlarge using coordinate points on the coordinate plane. Dilation assessmentanswer key analyze the coordinate plane and provide your answer in the space below. Recall from topic 7 that a dilation is not a rigid motion because size is not preserved.
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