Question

The sequence of transformations that can be performed on quadrilateral ABCD to show that it is congruent to quadrilateral GHIJ is a_____ followed by a______

first blank could be
A.reflection across the y-axis
B. 90 degree counterclockwise rotation around point A
C. 90 degree clockwise rotation around point A
D.90 degree counterclockwise rotation around point B

second blank could be
A.clockwise rotation about point B and a translation 20 units down
B.reflection across the y axis and a translation 20 units down
C.reflection across the x axis and a translation 15 units down
D.reflection across the y axis and a translation 25 units down

Answer 1

Blank 1.

B. 90 degree counterclockwise rotation around point A

Blank 2.

B.reflection across the y axis and a translation 20 units down

Answer 2

First transformation.

Duadrilateral ABCD has vertices with such coordinates:

• A(15,10);
• B(15,20);
• C(20,15);
• D(20,5).

Apply a rotation by 90°counterclockwise around point A to this quadrilateral, then

• A(15,10)→A'(15,10);
• B(15,20)→B'(5,10);
• C(20,15)→C'(10,15);
• D(20,5)→D'(20,15).

Second transformation.

1. A reflection across the y axis has a rule:

(x,y)→(-x,y).

Then

• A'(15,10)→A''(-15,10);
• B'(5,10)→B''(-5,10);
• C'(10,15)→C''(-10,15);
• D'(20,15)→D''(-20,15).

2. A translation 20 units down has a rule:

(x,y)→(x,y-20).

Then

• A''(-15,10)→G(-15,-10);
• B''(-5,10)→H(-5,-10);
• C''(-10,15)→I(-10,-5);
• D''(-20,15)→J(-20,-5).

Answer: first blank -B, second blank - B.