Unit 2, Lesson 10
Dilations on a Square Grid
Accelerated 7
10.1
Warm-up
Point is the dilation of point with center of dilation and scale factor .
Estimate . Be prepared to explain your reasoning.
10.2
Activity
- Draw the image of quadrilateral after a dilation with center and scale factor 2.
- Draw the image of triangle after a dilation with center T and scale factor 2.
- Draw the image of triangle after a dilation with center T and scale factor .
Point T, triangle Q R S and three projection rays on a square grid. Let the lower left corner be (0 comma 0). Then triangle Q R S is Q(5 comma 7), R(6 comma 5), S(4 comma 4) and point T is T(2 comma 6). The dashed projection rays are T Q, T R and T S.
Student Lesson Summary
Square grids can be useful for showing dilations, especially when the center of dilation and the point(s) being dilated lie at grid points. Rather than using a ruler to measure the distance between the points, we can count grid units.
For example, the dilation of point with center of dilation and scale factor will be 6 grid squares to the left and 3 grid squares down from , since is 4 grid squares to the left and 2 grid squares down from . The dilated image is marked as .
Sometimes the square grid comes with coordinates, giving us a convenient way to name points. Sometimes the coordinates of the image can be found just using arithmetic, without having to measure.
For example, to perform a dilation with center of dilation at and scale factor 2 on the triangle with coordinates , , and , we can just double the coordinates to get , , and .
Two triangles on a coordinate plane, origin O. Horizontal axis scale negative 7 to 7 by 1’s. Vertical axis scale negative 5 to 5 by 1’s. The coordinates of the triangle are (negative 1 comma negative 2), (3 comma 1), (2 comma negative 1 ). The coordinates of the image are(negative 2 comma negative 4), (6 comma 2), (4 comma negative 2).
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