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  y = 12

Step-by-step explanation:

Triangles ABD and CBD are congruent, so DA = DC:

  3y +6 = 5y -18

  24 = 2y . . . . . . . . add 18-3y; next, divide by 2

  12 = y

Additional comment

In some variations of this question, you may be asked to solve for x. Since the angles are equal, you have ...

  3x -1 = 34 -2x  ⇒  5x = 35  ⇒  x = 7 . . . (consistent with ∠ABC = 40°)

g = (2, 2)

step-by-step explanation:

given the ratio is 1 : 1 then f is the midpoint of eg

let the coordinates of g = (x, y)

using the midpoint formula

(0 + x) = 1 ( multiply both sides by 2 )

0 + x = 2 ⇒ x = 2

similarly

(4 + y) = 3 ( multiply both sides by 2 )

4 + y = 6 ( subtract 4 from both sides )

y = 2

coordinates of g = (2, 2)

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step-by-step explanation: