# How to find the scale factor of a dilation of a circle

Play Scale Factor X at MathPlayground.com! Practice ratio, scale, and proportion. Section 9.5 Dilations Key Concept Dilation A dilation with center C and scale factor n, n > 0, is a transformation with these two properties: The image of Cis itself (that is, C' = C). • For any other point R, R' is on CR and CIR' CR' The image of a dilation is similar to its preimage. CR' = n.CR Hit Main Image Browse and select an image containing a known measurement. Click and drag in the image to measure a known width or height. Enter this actual (full scale) known width or height (inches) in the appropriate textbox and hit Set Width Scale or Set Height Scale to calculate and set the scale of the image. Circle with center G is dilated using a scale factor 2.0. Center of dilation is the center of the circle. Which of the following line will it touch now? A. x = −2: B. y = 22: C. y = 10: D. All of the above MCC9-12.G.SRT.1 Verify experimentally the properties of dilations given by a center and a scale factor: a. A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged. b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor. Scale Factor/ Dilation Factor Ratio formed when comparing the distance of the image from the center of dilation to the distance of the original figure from the center of dilation. (Like the ratio of inches to miles on a map!) dilation on a graph, Dilation is a transformation, that stretches or shrinks the original figure presented on the grid based on the scale factor. Included here are umpteen printable worksheets to help 8th grade and high school students hone in on finding the scale factor, identifying the dilation type, determining the new coordinates and drawing the dilated shapes with the center as origin. The above question is pretty simple, and I used common sense to figure out that the coordinates (3, -7) is the answer, since it is the only viable spot. I was wondering how I would find the scale ... Textbook solution for Geometry, Student Edition 1st Edition McGraw-Hill Chapter 9.6 Problem 33PPS. We have step-by-step solutions for your textbooks written by Bartleby experts!Produce a scale drawing of XYZ with point X as the center and a scale factor of ¼ . Use the dilation theorem to predict Y'Z', and then measure its length directly using a ruler. This video shows show to dilate a triangle on the coordinate plane by a scale factor of 1/2 and by a scale factor of 2/3. The scaling is uniform if and only if the scaling factors are equal (v x = v y = v z). If all except one of the scale factors are equal to 1, we have directional scaling. In the case where v x = v y = v z = k, the scaling is also called an enlargement or dilation by a factor k, increasing the area by a factor of k 2 and the volume by a factor ... b. Dilation a scale factor of 2 and then rotation of IBO degrees. c. Dilation by scale factor of 3 and then another dilation by a scale factor of 1/3. Complete the table below and graph both the original (pre-image and Image pre-Image Process 8. Length of Sides: How did the following change? A. Angle Measures: Dilations in the Coordinate Plane. WordsTo dilate a ﬁ gure with respect to the origin, multiply the coordinates of each vertex by the scale factor k. Algebra (x, y) (kx, ky) When k> 1, the dilation is an enlargement. When k> 0 and k< 1, the dilation is a reduction. Sur> Tet> MMESH3d ( Simone Marras ) : A Semi-structured Multiblock (2 Blocks In Z) 2D/3D Mesh Generator For Hexahedrons And Prisms --wedges Of Triangular Base-- In 3d, And Quads A Find the scale factor. Tell whether the dilation is a or an enlargement Then find the values of the variables. Use the origin as the center of the dilation and the given scale factor to find the coordinates of the vertices of the image of the polygon. A dilation maps A to A' and B to B' Find the center of the dilation. When the scale factor of the dilation(s) is not equal to 1 or −1, similarity transformations preserve angle measure only. Performing a Similarity Transformation Graph △ABCwith vertices A(−4, 1), B(−2, 2), and C(−2, 1) and its image after the similarity transformation. Translation:(x,y) → (x + 5,y + 1) The scale factor 0.25 is less than 1, so the dilation is a(n) enlargement / reduction . 20. Image length 5 scale factor ∙ original length, so image height 5 ? , or cm. Know Need Plan Coordinates of vertices: P(2, 0), Z( , ), and G( , ) Center of dilation: ( , ) Scale factor: Coordinates of the images of the vertices Substitute the coordinates • Dilations require a center of dilation and a scale factor. • The center of dilation is the point about which all points are stretched or compressed. • The scale factor of a figure is a multiple of the lengths of the sides from one figure to the transformed figure. • Side lengths are changed according to the scale factor, k. Similarity: Dilations Similar objects are objects that have the same shape, but are not necessarily the same size. Dilations are an example of two objects that are the same shape, but different sizes. Dilations vary in size by a set scale factor. Dilation usually affect the size of an object along one line. ... Math Worksheets Author: The center of circle Cʹ coincides with point . B Transform circle Cʹ with the dilation with center of dilation and scale factor _sr . Circle Cʹ is made up of all the points at distance from point . After the dilation, the image of circle Cʹ will consist of all the points at distance from point D. A dilation that makes a larger image than the original is known as enlargement. A dilation that makes a smaller image than the original is referred as reduction. Use our simple online center of dilation calculator to find the value if the same with ease. The amount of scaling is given by the scale factor (greater than zero) If the scale factor is less than 1, the figure is reduced and it is sometimes called a contraction If the scale factor is... Dilations Guided Practice A _____ is a type of transformation that changes the size of a figure by a scale factor. 1. Find the scale factor of the triangle. 2. Circle open applet in presentation mode. Complete the table. In the row labeled S, write the distance between. P. and the point on the smaller circle in grid units. In the row labeled L, write the distance between. P. and the corresponding point on the larger circle in grid units. A square with a perimeter of 20 units is graphed on a coordinate grid. The square is dilated by a scale factor of 0.4 with the origin as the center of dilation. If (x, y) represents the location of any point on the original square, which ordered pair represents the coordinates of the corresponding point on the resulting square? For the given dilation, find the scale factor. Then decide whether the dilation is an enlargement or a reduction. Example For the given dilation, find the scale factor. Then decide whether the dilation is an enlargement or a reduction. Got It? Which graph shows a dilation? Example Circle the transformation that is a dilation. the scale factor used to create W’X’Y’Z’ 11. Us the origin as the center of the dilation and the given scale factor to find the coordinates of the vertices of the image of the polygon and draw that image on the coordinate plane, scale factor = 2.5. C’ = ( 12. Consider the following diagram: A. Scale factor Similar figures are identical in shape, but generally not in size. A missing length on a reduction/enlargement figure can be calculated by finding its linear scale factor. In the diagram, the circle will be dilated by a scale factor of 3 about the origin. The points C, A, and B map to C', A', and B' after the dilation. What is the length of C' B' ? Use the distance formula to help you decide.Standard 7.G.1: Solve problems involving scale drawings of geometric figures, such as computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. Concepts and Skills to Master • Use a scale or scale factor to find a measurement. The scale factor is commonly expressed as 1:n or 1/n, where n is the factor. For example, if the scale factor is 1:8 and the real measurement is 32, divide 32 ÷ 8 = 4 to convert. To convert a measurement to a larger measurement simply multiply the real measurement by the scale factor. For example, if the scale factor is 1:8 and the measured ... Since the scale factor is 2, the corresponding point in the image B' is twice that distance from O and lying on the same line, so OB' is 2 times 12, or 24. Note that if the scale factor is less than 1, then the image points are closer to the center of dilation to create an image smaller than the original. _____11) dilation image with scale factor . 1 3 of (6, –3) 12. Pick an original angle in 1-7 problem above, circle it.