Question

1. triangle abc is transformed to create triangle abc.

verbal description:
algebraic rule:

Explanation:

Step1: Find coordinates of points

Find coordinates of \(A(-5,1)\), \(B(-4,6)\), \(C(-1,3)\) and \(A'(5,-1)\), \(B'(4,-6)\), \(C'(1,-3)\).

Step2: Determine the transformation rule

For \(x\)-coordinate: \(x\to -x\) (e.g., \(-5\to5\), \(-4\to4\), \(-1\to1\)). For \(y\)-coordinate: \(y\to -y\) (e.g., \(1\to - 1\), \(6\to - 6\), \(3\to - 3\)).

Answer:

The algebraic rule is \((x,y)\to(-x,-y)\) (a rotation of \(180^{\circ}\) about the origin). The verbal description is: Triangle \(ABC\) is rotated \(180^{\circ}\) about the origin to form triangle \(A'B'C'\).