Question

1. in the diagram, figure g is congruent to figure g. what sequence of transformations can be performed to show that the figures are congruent? show your work. 4. figure b is in quadrant iv. it is reflected across the x - axis to form figure b. then figure b is rotated 90° counterclockwise around the origin to form figure b. then figure b is translated 4 units to the left to form figure b. decide if each statement about the figures is true or false. choose true or false for each statement. a. figure b is in quadrant ii. b. figure b is in quadrant iii. c. the x - coordinates for the vertices of b are all negative. d. the y - coordinates for the vertices of b are all positive.

Explanation:

Step1: Analyze reflection of Figure B

When Figure B in Quadrant IV is reflected across the x - axis to form Figure B', the transformation rule for reflection across the x - axis is $(x,y)\to(x, - y)$. So Figure B' is in Quadrant I.

Step2: Analyze rotation of Figure B'

When Figure B' is rotated 90° counter - clockwise around the origin to form Figure B'', the transformation rule for a 90° counter - clockwise rotation around the origin is $(x,y)\to(-y,x)$. So Figure B'' is in Quadrant II.

Step3: Analyze translation of Figure B''

When Figure B'' is translated 4 units to the left to form Figure B''', the transformation rule is $(x,y)\to(x - 4,y)$. Since Figure B'' is in Quadrant II, after translation 4 units to the left, Figure B''' is still in Quadrant II. The x - coordinates of vertices of B''' are all negative and the y - coordinates are all positive.

Answer:

a. True
b. False
c. True
d. True