Learning path
Dilations and Similarity - Grade 8
Explore dilations and similarity on the coordinate plane. Practice finding scale factors, working with various centers of dilation, analyzing transformations, and evaluating changes in geometric properties.
Exercises in this learning path
20 exercises-
1
Understanding Scale Factors of Dilation
Explore how scale factors enlarge or reduce geometric figures. Practice applying scale factors to determine image dimensions and properties.
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2
Dilations Centered at the Origin
Practice dilating points and shapes on the coordinate plane when the center of dilation is at the origin. Multiply coordinate values by scale factors to find new positions.
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3
Finding Original Coordinates (Pre-Image)
Work backward from a dilated image to determine the coordinates of the original pre-image. Use the scale factor and image points to calculate original coordinates.
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4
Identifying Scale Factor from Coordinate Pairs
Compare pre-image and image coordinate pairs to find the scale factor of a dilation. Analyze corresponding coordinates on the coordinate plane.
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5
Dilations Centered at Non-Origin Points
Perform dilations when the center of dilation is located at points other than the origin. Calculate transformed coordinates relative to fixed non-origin points.
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6
Similarity and Dilations on Coordinate Plane
Examine how dilations produce similar figures on the coordinate plane. Identify proportional side lengths and corresponding angle relationships.
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7
Perimeter and Area Changes Under Dilation
Discover how scaling a figure affects its perimeter and area on the coordinate plane. Calculate changes in perimeter and area using given scale factors.
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8
Dilating Line Segments and Distance
Measure and calculate distance changes when line segments undergo a dilation. Analyze segment lengths before and after scaling transformations.
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9
Slope and Parallelism in Dilated Lines
Investigate how dilations preserve slope and maintain parallelism between lines. Practice determining the slopes and equations of dilated lines.
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10
Combinations: Dilation and Translation
Apply sequential transformations involving both a dilation and a translation. Track how coordinate values change through combined transformation steps.
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11
Combinations: Dilation and Reflection/Rotation
Explore multi-step transformations that combine dilations with reflections or rotations. Determine final coordinates after applying rigid motions alongside scaling.
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12
Dilations in Real-World Coordinate Scenarios
Solve practical scenarios that model dilations on a coordinate grid. Apply scale factors and coordinate transformations to contextual problems.
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13
Determining Center of Dilation
Locate the center of dilation given a pre-image and its dilated image on a coordinate plane. Use lines connecting corresponding points to find the center.
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14
Fractional and Rational Scale Factors
Perform dilations using fractional and rational scale factors. Calculate new coordinates accurately when enlarging or shrinking figures by rational multiples.
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15
Similarity Proofs on Coordinate Plane
Verify geometric similarity between figures on the coordinate plane using transformations. Show similarity through proportional side lengths and coordinate relationships.
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16
Dilations with Negative Coordinates
Practice applying dilations to points and figures located in quadrants with negative coordinate values. Apply scale factors correctly across all coordinate quadrants.
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17
Center of Dilation at Polygon Vertices
Perform dilations of polygons where a vertex of the shape serves as the center of dilation. Calculate the resulting coordinates for the remaining vertices.
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18
Dilation of Circles on Coordinate Plane
Scale circles on the coordinate plane by altering their radii according to a given scale factor. Determine new equations, radii, and positions of dilated circles.
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19
Dilation Matrix Concepts for Grade 8
Learn basic matrix concepts used to represent and calculate dilations on the coordinate plane. Apply scalar multiplication to coordinate matrices.
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20
Comprehensive Review of Dilation and Similarity
Review key concepts of dilations, scale factors, centers of dilation, and similarity. Test your understanding through a comprehensive set of summary problems.
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