The scale factor can be found by comparing the corresponding side lengths of the two triangles.
For the small triangle ABC, the lengths of the sides are:
AB = sqrt[(3-2)^2 + (2-1)^2] = sqrt[1+1] = sqrt(2)
BC = sqrt[(1-3)^2 + (3-2)^2] = sqrt[4+1] = sqrt(5)
AC = sqrt[(1-2)^2 + (3-1)^2] = sqrt[1+4] = sqrt(5)
For the large triangle A'B'C', the lengths of the sides are:
A'B' = sqrt[(9-6)^2 + (6-3)^2] = sqrt[9+9] = sqrt(18)
B'C' = sqrt[(3-9)^2 + (9-6)^2] = sqrt[36+9] = sqrt(45)
A'C' = sqrt[(3-6)^2 + (9-3)^2] = sqrt[9+36] = sqrt(45)
To find the scale factor, we can compare the ratios of the side lengths:
AB/A'B' = (sqrt(2))/(sqrt(18)) = sqrt(2/18) = sqrt(1/9) = 1/3
BC/B'C' = (sqrt(5))/(sqrt(45)) = sqrt(5/45) = sqrt(1/9) = 1/3
AC/A'C' = (sqrt(5))/(sqrt(45)) = sqrt(5/45) = sqrt(1/9) = 1/3
Since all the ratios are equal to 1/3, the scale factor of the dilation between the preimage ABC and image A'B'C' is 1/3.
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)
1 answer
1 answer