Question

b. dilate each figure or answer the question using the information provided. then, compare and contrast the corresponding angles and side lengths of the original figure and dilated figure. in addition, compare the area of the original figure to the area of the dilated figure. finally, write the algebraic representation for a dilation of the point (x, y) using the given scale factor.

1. triangle def is the image that resulted from a dilation of △abc using the origin as the center of dilation. what scale factor was used to dilate △abc?

the corresponding angles are all
original side length : new side length is
the coordinates of a ( )
the coordinates of d ( )
scale factor = \\(\frac{new}{original}=\frac{}{}=\\)
the area of △abc is 4 units²
the area of △def is 4 x = unit²
the algebraic representation is ( )

Explanation:

Step1: Identify angle - property

In dilation, corresponding angles are congruent.

Step2: Determine side - length ratio

Count grid - squares for side - length comparison.

Step3: Read coordinates

Read A and D coordinates from graph.

Step4: Calculate scale factor

Use formula with coordinates of corresponding points.

Step5: Recall area relationship

Area of dilated figure is scale - factor² times original area.

Step6: Write algebraic representation

Multiply x and y coordinates of original point by scale factor.

Answer:

The corresponding angles are all equal.
Original Side Length : New Side Length is 1:2.
The coordinates of A(2,2).
The coordinates of D(4,4).
Scale Factor = $\frac{new}{original}=\frac{4 - 2}{2 - 0}= 2$.
The area of $\triangle ABC$ is 4 units².
The area of $\triangle DEF$ is 4×4 = 16 unit².
The algebraic representation is (2x,2y).