(20 PTS) Someone explain to me why this is the case

i is an imaginary number because i = and you can never take a square root of a negative number.  Because i is equal to when you square it it just removes the square root sign and gives you -1

Step-by-step explanation:

1. For similar triangles, the ratio of the corresponding sides is constant.
In this case, AD corresponds to EH, while AB corresponds to EF.
Therefore; AD/EH = AB/EF
  45/75 = 30/ EF
        EF = (30×75)/45
             = 50 in

2. Triangle DEF is not congruent ABC.
For congruent triangles; if three pairs of sides are equal in length, then the triangles are congruent. Also triangles are congruent if two pairs of angles of the triangle are equal in measurement, and the included sides are equal in length, then the triangles are congruent. 

3. Triangle ABC is rotated 90° clockwise, and then reflected over the line y=x to form triangle DEF. This description is Congruent.
Triangle ABC is reflected over the x-axis, and then dilated by a factor of 12 to form triangle DEF. Description not congruent
Triangle ABC is rotated 180° , and then translated 4 units down and 2 units right to form triangle DEF. The description is Congruent

4. A point (-1,10) is rotated 90° counterclockwise about the origin.
The resulting coordinates of the image is (-10,-1)
A rotation through 90 about the origin is anticlockwise (counter clockwise direction)