Chapter 11.8, Problem 24STP

To determine

To find:What is the ratio comparing the lengths of the sides of Figure A to Figure B.

Answer to Problem 24STP

Ratio comparing the lengths of the sides of figure A to Figure B is $\frac{4}{3}$

Explanation of Solution

Given information:

Figure A is reflected over the Y-axis and then dilated by a scale factor of $\frac{3}{4}$ to get Figure B

We know that reflection does not change the size of the image.

Therefore, after reflection about Y-axis there no change in size of the image of Figure B.

It means Dimensions of Figure A and Figure B will be same after reflection over Y-axis.

Now after reflection dilation has occurred by a scale factor of $\frac{3}{4}$ .

We know

Scale factor $=\frac{I}{P}$

Where

  $I=$ length of image

  $P=$ length of preimage.

  $\Rightarrow$ Scale factor $=\frac{B}{A}$

Where

  $B=$ length of Figure B

  $A=$ length of Figure A.

  $\Rightarrow$ $\frac{3}{4}=\frac{B}{A}$

On inversing both sides

We get

  $\frac{A}{B}=\frac{4}{3}$

Therefore,

Ratio comparing the lengths of the sides of figure A to Figure B is $\frac{4}{3}$