Question

how will the coordinates of the vertices of
△abc compare to the coordinates of the
vertices of △abc?
in △abc, each ? will be
? the x - coordinate
y - coordinate

Explanation:

Step1: Analyze the transformation

Assume a reflection over the \(x\) - axis (common transformation when comparing original and image triangle in coordinate - plane problems). For a point \((x,y)\) reflected over the \(x\) - axis, the transformation rule is \((x,y)\to(x, - y)\).

Step2: Compare coordinates

In \(\triangle A'B'C'\), if it is a reflection of \(\triangle ABC\) over the \(x\) - axis, for each vertex:

• The \(x\) - coordinate remains the same.
• The \(y\) - coordinate is the opposite (negative) of the \(y\) - coordinate of the corresponding vertex in \(\triangle ABC\).

Answer:

In \(\triangle A'B'C'\), each \(y\) - coordinate will be the opposite of the \(y\) - coordinate of the corresponding vertex in \(\triangle ABC\) (while \(x\) - coordinates remain the same).