Question

△abc is reflected to form △abc.
the coordinates of point a are (-4, -3), the coordinates of point b are (-7, 1), and the coordinates of point c are (-1, -1).
which reflection results in the transformation of △abc to △abc?
o reflection across the x - axis.
o reflection across the y - axis

Explanation:

Step1: Recall reflection rules

• Reflection across the \(x -\)axis: \((x,y)\to(x, - y)\)
• Reflection across the \(y -\)axis: \((x,y)\to(-x,y)\)

Step2: Apply reflection rules to a sample point

Let's assume we check the reflection of a general point \((x,y)\).
If we consider reflection across the \(x -\)axis:
Take a point \((a,b)\). After reflection across the \(x -\)axis, it becomes \((a,-b)\).
If we consider reflection across the \(y -\)axis: \((a,b)\to(-a,b)\)

Let's check for point \(C\). Suppose in \(\triangle ABC\), if we assume the reflection is across the \(x -\)axis.
Let the original coordinates of \(C\) be \((x,y)\). After reflection across the \(x -\)axis \((x,y)\to(x, - y)\).
If we assume the original point \(C\) has coordinates \((- 1,1)\) (before reflection across the \(x -\)axis, the reflected point \(C'\) is \((-1,-1)\)

Answer:

reflection across the \(x -\)axis.