Chapter 9, Problem 9STP

To determine

To calculate:To describe the transformation of the below coordinate plane -

  

Answer to Problem 9STP

The triangles are similar.

  $\Delta DEF\sim \Delta D^{\text{'}}{E}^{\text{'}}{F}^{\text{'}}$

And ratio of sides of the triangles are equal:

  $\frac{DE}{D^{\text{'}}{E}^{\text{'}}}=\frac{EF}{E^{\text{'}}{F}^{\text{'}}}=\frac{DF}{D^{\text{'}}{F}^{\text{'}}}$

Explanation of Solution

Given information:

Given coordinate below is:

  

Formula Used:

If the angles of two triangles are equal, then the triangles are similar and thus the ratio of sides are equal.

Calculation:

From the below coordinate, we have:

  

Angles of both the triangles are equal.

Thus, the triangles are similar.

  $\Delta DEF\sim \Delta D^{\text{'}}{E}^{\text{'}}{F}^{\text{'}}$

And thus the ratio of sides of the triangles are equal:

  $\frac{DE}{D^{\text{'}}{E}^{\text{'}}}=\frac{EF}{E^{\text{'}}{F}^{\text{'}}}=\frac{DF}{D^{\text{'}}{F}^{\text{'}}}$

Conclusion:

Thus, the triangles are similar.

  $\Delta DEF\sim \Delta D^{\text{'}}{E}^{\text{'}}{F}^{\text{'}}$

And ratio of sides of the triangles are equal:

  $\frac{DE}{D^{\text{'}}{E}^{\text{'}}}=\frac{EF}{E^{\text{'}}{F}^{\text{'}}}=\frac{DF}{D^{\text{'}}{F}^{\text{'}}}$