Parallelogram F"G"H"J" is the final image after the rule
was applied to parallelogram FGHJ.

Parallelogram F double-prime G double-prime H double-prime J double-prime has points (3, 4), (2, 2), (4, 2), (5, 4).
What are the coordinates of vertex F of parallelogram

(-4,2)

Step-by-step explanation:

r (y-axis) o T1,2 (x,y)

This Composition of Transformations

So, first we will make T1,2 (x,y) then r (y-axis)

Let the coordinates of vertex F ⇒(x,y)

The rule of translation T₁,₂ is (x,y)→(x+1,y+2)

So, After translation from F to F' the point  F' = (x+1,y+2)

The rule of reflection over y-axis is (x,y)→(-x,y)

So, After reflection F' over y-axis F'' = (-[x+1] , y+2)

But F'' from the graph = (3,4)

∴ (-[x+1] , y+2) = (3,4)

∴ -(x + 1) = 3  and  y + 2 = 4

-x - 1 = 3       |   y + 2 = 4

-x = 4          |    y = 2

x = -4            |

∴ (x,y) = (-4,2)

So, the coordinates of vertex F is (-4,2)

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