Questions: Name: Dilations Problems 1-2 Use the dilation rule written in coordinate f 1. Identify the scale factor and center of dilation from the dilation rule. (x, y) → (3(x+4)-4,3(y+3)-3) Scale factor: Center of dilation:

Solution Steps

The dilation rule given is \((x, y) \rightarrow (3(x + 4) - 4, 3(y + 3) - 3)\). To identify the scale factor, observe the coefficients of \(x\) and \(y\) in the transformation. The coefficients are both 3, indicating that the scale factor is 3.

To find the center of dilation, set the transformed coordinates equal to the original coordinates and solve for the center \((h, k)\): \[ (x, y) \rightarrow (3(x + 4) - 4, 3(y + 3) - 3) \] \[ (x, y) \rightarrow (3x + 12 - 4, 3y + 9 - 3) \] \[ (x, y) \rightarrow (3x + 8, 3y + 6) \] The center of dilation \((h, k)\) is the point that remains invariant under the transformation. By setting the transformed coordinates equal to the original coordinates, we get: \[ 3(h + 4) - 4 = h \quad \text{and} \quad 3(k + 3) - 3 = k \] Solving these equations: \[ 3h + 12 - 4 = h \implies 2h + 8 = 0 \implies h = -4 \] \[ 3k + 9 - 3 = k \implies 2k + 6 = 0 \implies k = -3 \] Thus, the center of dilation is \((-4, -3)\).

To graph the image of the figure shown on the graph using the dilation rule, apply the transformation to each point of the figure. For example, if a point \(A\) has coordinates \((x, y)\), its image \(A'\) will have coordinates: \[ A' = (3(x + 4) - 4, 3(y + 3) - 3) \] Apply this transformation to each point of the figure and plot the new points on the graph.

Final Answer