Question

∆ABC rotates around point D to create ∆A′B′C′.

Answer 1

Answer:

A‘=（4，1）

A“=（11，8）

Step-by-step explanation:

A‘=（4，1）

A“=（11，8）

Answer 2

Answer:

The coordinates of A' are (4,1). Therefore the coordinates of A'' are (11,2).

Step-by-step explanation:

From the figure it is clear that the coordinates of triangle ABC are A(4,9), B(4,6) and C(2,6).

The ∆ABC rotates around point D to create ∆A′B′C′. The vertices of image are  B'(4,4) and C'(6,4).

From the figure it is clear that ∆ABC rotates 180° around point D to create ∆A′B′C′.

$(x,y)\rightarrow (-x+8,-y+10)$

The coordinates of A' are

$A(4,9)\rightarrow A'(-4+8,-9+10)=A'(4,1)$

The coordinates of A' are (4,1).

If ∆A′B′C′ rotates 90° counterclockwise around point E(7, 5) to form triangle ∆A″B″C″, then

$(x,y)\rightarrow (-y+12,x-2)$

The coordinates of A'' are

$A'(4,1)\rightarrow A''(-1+12,4-2)=A''(11,2)$

Therefore the coordinates of A'' are (11,2).