∆abc rotates around point d to create ∆a′b′c′.

based on the position of b'c', shown in the figure, the coordinates of a′ are (4,1)(4,7)(6,1)(6,7).

if ∆a′b′c′ rotates 90° counterclockwise around point e(7, 5) to form triangle ∆a″b″c″, the coordinates of a″ are (3,6)(7,2)(7,6)(11,2).

Given that ∆ABC rotates around point D to create ∆A′B′C′.
 
Line BC is a horizontal line such that the length of BC is 2 units. Also line AB is a vertical line such that the length of AB is 3 units.

Based on the position of B'C', shown in the figure, the coordinates of A′ are will be vertical to the cordinate of B' going downwards with a length of 3 units. This means that the x-value of the coordinate of A' is the same as that of B' but the y-value of the coordinate of A' is 3 units less than that of B'.

The coordinate of B' is (4, 4).
Therefore, the coordinate of A' is (4, 4 - 3) = (4, 1).

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Step-by-step explanation:

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