Question

1. a hexagon will be dilated on a coordinate grid. the hexagon is dilated using the origin as the center of dilation.

• write one scale factor that would result in a hexagon smaller than the original.
• write one scale factor that would result in a hexagon larger than the original.
• how did you know what the scale factor needed to be for each dilation?
• for a smaller hexagon, the scale factor must be
• for a larger hexagon, the scale factor must be

1. triangle abc is graphed on a coordinate grid with vertices at a(5, 3), b(3, - 3) and c(-2, 4). triangle abc is dilated by a scale factor of k with the origin as the center of dilation to create triangle abc. circle the ordered pair that represents the coordinates of the vertex c.

(5 + k, 3 + k) (-2 + k, 4 + k) (5k, 3k) (-2k, 4k)

1. circle a was dilated to create circle b. triangle pqr was dilated to create triangle pqr. rectangle mnop was dilated to create rectangle mnop. all figures were dilated with the origin as the center of dilation.

draw a line to each grid from the one algebraic representation that correctly describes the dilation.
(x, y)→(2x, 2y) (x, y)→(1/2x, 1/2y) (x, y)→(1/3x, 1/3y) (x, y)→(3x, 3y)

Explanation:

Step1: Determine scale - factor for smaller hexagon

When the scale - factor \(k\) of a dilation is between \(0\) and \(1\) (i.e., \(0

Step2: Determine scale - factor for larger hexagon

When the scale - factor \(k>1\), the dilated figure is larger than the original. For example, \(k = 2\).

Step3: Find coordinates of \(C'\) after dilation

When a point \((x,y)\) is dilated with the origin as the center of dilation and a scale - factor \(k\), the new coordinates \((x',y')=(kx,ky)\). Given \(C(-2,4)\) and scale - factor \(k\), the coordinates of \(C'\) are \((-2k,4k)\).

Step4: Match dilation rules with figures

For a dilation with scale - factor \(2\), the rule is \((x,y)\to(2x,2y)\) (enlargement). For a dilation with scale - factor \(\frac{1}{2}\), the rule is \((x,y)\to(\frac{1}{2}x,\frac{1}{2}y)\) (reduction). For a dilation with scale - factor \(\frac{1}{3}\), the rule is \((x,y)\to(\frac{1}{3}x,\frac{1}{3}y)\) (reduction). For a dilation with scale - factor \(3\), the rule is \((x,y)\to(3x,3y)\) (enlargement).

Answer:

2.

• Scale factor for smaller hexagon: \(\frac{1}{2}\)
• Scale factor for larger hexagon: \(2\)
• For a smaller hexagon, the scale factor must be between \(0\) and \(1\). For a larger hexagon, the scale factor must be greater than \(1\).

1. \((-2k,4k)\)
2. Match based on the size change of the figures. If the figure is enlarged, it corresponds to a scale - factor greater than \(1\) (e.g., \((x,y)\to(2x,2y)\) or \((x,y)\to(3x,3y)\)). If the figure is reduced, it corresponds to a scale - factor between \(0\) and \(1\) (e.g., \((x,y)\to(\frac{1}{2}x,\frac{1}{2}y)\) or \((x,y)\to(\frac{1}{3}x,\frac{1}{3}y)\)).