Scale Factor and Dilations Worksheets Grade 10

1. Hana is a landscape architect designing a triangular garden bed. The original design on her coordinate grid has vertices at A(12, 9), B(18, 21), and C(24, 3). To create a larger version for a public park, she applies a dilation centered at the origin with a scale factor of 4. What are the coordinates of vertex B' after this dilation?
2. Dilate point (9, 12) by scale factor 2/3 from center (3, 4)
3. A cartographer is creating a detailed map of a national park. The original blueprint of the park's main trail system is drawn on a coordinate grid. The triangular region formed by points A(2, 4), B(6, 8), and C(10, 2) represents a forested area. To fit this region onto the final map, the cartographer applies a dilation centered at the origin with a scale factor of 2.5. What are the coordinates of the vertices of the dilated triangular region?

…and 4 more problems

1. Aroha dilates point (3, 7) by scale factor 5 from center (1, 1). Find the new coordinates.
2. A graphic designer is creating a logo that will be printed on business cards and large banners. The original logo design is a triangle with vertices at (0,0), (4,0), and (2,3). For the banner, she applies a dilation centered at the origin with a scale factor of 2.5. What are the coordinates of the dilated triangle's vertices?
3. Dilate point (7,12) by scale factor 2 from origin = ?

…and 5 more problems

1. Dilate point (4, 8) by scale factor 2 from center (0, 0)
2. An architect is designing a new building and creates a scale model where the model's height is 1.5 meters. The actual building will be 45 meters tall. If the volume of the model is 0.8 cubic meters, what will be the volume of the actual building in cubic meters?
3. Dilate point (4,6) by scale factor 2 from origin

…and 5 more problems