Question

Find the value of variable a given the transformation is an isometry.

Answer 1

Answer:

• a =10

,

• b = 4

Explanation:

An isometry is a rigid transformation that preserves length and angle measures, as well as perimeter and area.

This means that the two right triangles are congruent.

Thus, we have that:

`\begin{gathered} 3a=30 \\ 10b=40\degree \end{gathered}`

Next, we solve for a and b.

`\begin{gathered} 3a=30 \\ \text{Divide both sides by 3} \\ (3a)/(3)=(30)/(3) \\ a=10 \end{gathered}`

Likewise:

`\begin{gathered} 10b=40\degree \\ \text{Divide both sides by 10} \\ (10b)/(10)=(40\degree)/(10) \\ b=4 \end{gathered}`

The values of a and b are 10 and 4 respectively.