To plot the new house using dilation with a scale factor of 2 from the original coordinates you provided, we first identify the original coordinates and then apply the dilation transformation.
Original Coordinates:
- \(A(-4, 0)\)
- \(B(-4, 4)\)
- \(C(-2, 6)\)
- \(D(0, 4)\)
- \(E(0, 0)\)
Dilation Transformation: When we perform a dilation with a scale factor of 2, we multiply each coordinate by 2.
New Coordinates:
- \(A'(-4 \times 2, 0 \times 2) = (-8, 0)\)
- \(B'(-4 \times 2, 4 \times 2) = (-8, 8)\)
- \(C'(-2 \times 2, 6 \times 2) = (-4, 12)\)
- \(D'(0 \times 2, 4 \times 2) = (0, 8)\)
- \(E'(0 \times 2, 0 \times 2) = (0, 0)\)
Coordinates After Dilation:
- \(A'(-8, 0)\)
- \(B'(-8, 8)\)
- \(C'(-4, 12)\)
- \(D'(0, 8)\)
- \(E'(0, 0)\)
For the graph, you could choose a color such as blue to plot these new points.
Congruence: The new house after this transformation is not congruent to the original house.
Reason:
- Congruent figures have the same shape and size. In this case, the new house is twice the size of the original house. The process of dilation enlarges the shape but does not preserve its size. Hence, while the shapes are similar, they are not congruent.