Question

geometry unit 6 lesson 2 homework name date period a sequence of transformations of qrst is shown on the coordinate grid. qrst is rotated then dilated, where qrst is the rotation and qrst is the dilation of qrst. 1. complete the descriptions: qrst was ____ to create qrst. 2. qrst was dilated using a scale factor of __ centered at ____ to create qrst. 3. complete the table: dilation rotation transformation (x,y)→(3x + 3y) (x,y)→(y - x) algebraic description

Explanation:

Step1: Analyze dilation rule

For dilation, if the algebraic rule for dilation is \((x,y)\to(3x + 3y)\), we can assume a general point \((x,y)\) in the pre - image. When dilating a figure to get a new figure, the scale factor \(k\) can be found by looking at the transformation of the coordinates. If the transformation of a point \((x,y)\) to \((kx,ky)\) represents dilation centered at the origin. Here, if we assume the dilation is centered at the origin and the transformation is \((x,y)\to(3x,3y)\) (ignoring the incorrect form in the table for a moment as it should be two separate coordinates), the scale factor \(k = 3\).

Step2: Analyze rotation rule

For rotation, if the rule is \((x,y)\to(y,-x)\), this represents a \(90^{\circ}\) counter - clockwise rotation about the origin.

1. Description of transformations:

• The rotation is a \(90^{\circ}\) counter - clockwise rotation about the origin. The dilation is a dilation centered at the origin with a scale factor of \(3\).

1. Scale factor for dilation:

• The scale factor for the dilation of \(Q'R'S'T'\) to \(Q''R''S''T''\) is \(3\).

1. Complete the table:

• For dilation: \((x,y)\to(3x,3y)\)
• For rotation: \((x,y)\to(y,-x)\)

Answer:

1. Rotation: \(90^{\circ}\) counter - clockwise rotation about the origin; Dilation: Dilation centered at the origin with scale factor \(3\)
2. \(3\)
3. Dilation: \((x,y)\to(3x,3y)\); Rotation: \((x,y)\to(y,-x)\)