Use the image to answer the question.
A coordinate grid of quadrant 1 shows 2 plotted triangles of the same shape but different sizes. The x and y axes range from 0 to 10 in unit increments. A small tilted triangle upper A upper B upper C is formed by connecting the following plots: point upper A is left parenthesis 2 comma 1 right parenthesis; point upper B is left parenthesis 3 comma 2 right parenthesis; and point upper C is left parenthesis 1 comma 3 right parenthesis. A large tilted dotted triangle is formed by connecting the following plots: point upper A prime is left parenthesis 6 comma 3 right parenthesis; point upper B prime is left parenthesis 9 comma 6 right parenthesis; point upper C prime is left parenthesis 3 comma 9 right parenthesis.
What is the scale factor of a single dilation between the preimage ABC and image A′B′C′ ?
(1 point)
The scale factor can be found by comparing the corresponding side lengths of the two triangles.
For the small triangle ABC, the length of side AB is 3 units, the length of side BC is 2 units, and the length of side AC is 2 units.
For the large triangle A'B'C', the length of side A'B' is 3 units, the length of side B'C' is 2 units, and the length of side A'C' is 2 units.
Thus, the scale factor of a single dilation between the preimage ABC and image A'B'C' is 1.
wrong
Apologies for the incorrect response earlier.
To find the scale factor of a dilation, we can compare the corresponding side lengths of the two triangles.
For the small triangle ABC, the length of side AB is 3 units, the length of side BC is 2 units, and the length of side AC is 2.236 units (calculated using the distance formula).
For the large triangle A'B'C', the length of side A'B' is 3 units, the length of side B'C' is 2 units, and the length of side A'C' is 7.071 units (calculated using the distance formula).
To find the scale factor, we can divide the corresponding side lengths of the large triangle by the corresponding side lengths of the small triangle.
AB' / AB = 3 / 3 = 1
BC' / BC = 2 / 2 = 1
AC' / AC = 7.071 / 2.236 ≈ 3.162
Therefore, the scale factor of a single dilation between the preimage ABC and image A'B'C' is approximately 3.162.
still wrong
My apologies again for the incorrect response.
To find the scale factor of a dilation, we can compare the lengths of corresponding sides.
For the small triangle ABC, the length of side AB is 3 units, the length of side BC is 2 units, and the length of side AC is approximately 2.236 units (calculated using the distance formula).
For the large triangle A'B'C', the length of side A'B' is 3 units, the length of side B'C' is 4 units, and the length of side A'C' is approximately 8.062 units (calculated using the distance formula).
To find the scale factor, we can divide the corresponding side lengths of the large triangle by the corresponding side lengths of the small triangle.
AB' / AB = 3 / 3 = 1
BC' / BC = 4 / 2 = 2
AC' / AC = 8.062 / 2.236 ≈ 3.605
Therefore, the scale factor of a single dilation between the preimage ABC and image A'B'C' is approximately 3.605.