Question

for exercise 16, use the graph. 16. determine if the two figures are congruent. if they are congruent, what transformation(s) could map figure a onto figure b? if they are not congruent, what makes them incongruent? (lesson 4)

Explanation:

Step1: Check side - lengths

Use the distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$ or count grid - squares for horizontal and vertical sides. For Figure A, the vertical side lengths and horizontal side lengths can be counted. For Figure B, do the same. We find that the corresponding side - lengths of Figure A and Figure B are equal.

Step2: Check angles

By observing the orientation of the figures on the grid, we can see that the corresponding angles are equal. Since both side - lengths and angles are equal, the figures are congruent.

Step3: Determine transformation

A translation followed by a rotation can map Figure A onto Figure B. First, translate Figure A to the right by a certain number of units to align the horizontal position. Then, rotate Figure A around a point to match the orientation of Figure B.

Answer:

The two figures are congruent. A translation followed by a rotation can map Figure A onto Figure B.