1.
So on the first question, it does appear that these triangles are similar by SSS. However, we need to do ratios to prove that. Remember that similar figures have proportional sides, and if these triangles are similar, they will all have the same ratio.
[tex] \frac{40}{96} =\frac{96-57}{96} =\frac{44}{64+44} \\ \\ \frac{40}{96}=\frac{39}{96} =\frac{44}{108} [/tex]
If you divide these fractions, you will see that they are all different ratios, therefore the correct answer is A. not similar.
2.
So firstly, we should convert these fractions into improper fractions and have them under fourths to make this look easier.
To convert a mixed fraction to a improper fraction, multiply the whole number by the denominator and add what's on the numerator for that to be your numerator. The results we get are 7/2 and 21/4.
Next, to make the denominator 4, multiply the denominator and the numerator of 7/2 by 2/2 to get 14/4.
Now the scale says that every 1/4" = 1'. Just count the numerators of both fractions and we see that the answer is going to be A. 14 ft by 21 ft
3.
Now for this, just see how many units it gets from 3 to 1 and from -4 to 0.
We see that it takes -2 units from 3 to 1, and since they are both x-coordinates, the first half of the image is x - 2 .
Next, it takes 4 units to get from -4 to 0. Since they are both y-coordinates, the second half of the image is y + 4.
Putting it together, your image is (x - 2, y + 4), or B.
