Question

triangle \\( \triangle a b c \\) is reflected across line \\( \ell \\) to create \\( \triangle a ^ { prime } b ^ { prime } c ^ { prime } \\).
what is the area of \\( \triangle a ^ { prime } b ^ { prime } c ^ { prime } \\)?
square units

Explanation:

Step1: Recall the property of reflection

Reflection is a rigid transformation. Rigid transformations (like reflection) preserve the shape and size of the figure. So, the area of \(\triangle ABC\) is equal to the area of \(\triangle A'B'C'\).

Step2: Calculate the area of \(\triangle ABC\)

The formula for the area of a right - triangle is \(A=\frac{1}{2}\times base\times height\). For right - triangle \(\triangle ABC\), assume the legs (since it's a right - triangle) are \(a = 3\) and \(b=4\) (we can get the length of \(AB\) as \(4\) from the reflection property, because corresponding sides of congruent triangles are equal). Then \(A=\frac{1}{2}\times3\times4\).

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Answer:

\(6\)