Help! Question is on the pic

  (4, 5)

Step-by-step explanation:

Dilation by factor d about point (a, b) effects the transformation ...

  (x, y) ⇒ d((x, y) -(a, b)) +(a, b)

  ⇒ (d(x-a) +a, d(y-b) +b)

  (x, y) ⇒ (dx +a(1-d), dy +b(1-d))

We have (x, y) = (3, 4) and (a, b) = (1, 2) and d=3/2. Filling in these numbers, we get ...

  (3, 4) ⇒ ((3/2)(3)+1(1-3/2), (3/2)(4)+2(1-3/2)) = (9/2 -1/2, 6 -1) = (4, 5)

Point E' is (4, 5).

If you look at the graph, you realize that E is (2, 2) from (1, 2). Dilation by a factor of 3/2 moves it to (3/2)(2, 2) = (3, 3) from (1, 2). So ...

  E' = (3+1, 3+2)

  E' = (4, 5)

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47