Question

check your understanding 1
describe the rule for the transformation in words and algebraically.

Explanation:

Step1: Analyze Graph Transformation

Observe the two triangles (pre - image and image). The transformation appears to be a rotation. Let's check the center of rotation (point E, likely the origin - like or a common vertex). The pre - image (triangle with vertices like B, C, E) and the image (triangle with vertices like B', C', E) show a 180 - degree rotation about point E (or the origin - related point).

Step2: Describe in Words

The transformation is a 180 - degree rotation about the point of intersection (let's say point E). For a 180 - degree rotation about a point \((h,k)\), the rule is \((x,y)\to(2h - x,2k - y)\). If we assume the center of rotation is the origin (or a point that simplifies to origin - like for this case, maybe E is at \((0,0)\) or a symmetric point), the algebraic rule for 180 - degree rotation about the origin is \((x,y)\to(-x,-y)\). But from the graph, the rotation is 180 degrees about the point (let's assume the center is a point, say, the intersection point of the two triangles, and the rotation is 180 degrees, so the rule in words: Rotate the pre - image 180 degrees about the common vertex (point E) to get the image. Algebraically, if the center of rotation is \((h,k)\), for a 180 - degree rotation, \((x,y)\to(2h - x,2k - y)\). If we assume the center is \((0,0)\) (for simplicity, as the graph seems symmetric), the rule is \((x,y)\to(-x,-y)\). But more accurately, from the graph's symmetry, it's a 180 - degree rotation about the point of intersection (the common vertex), so in words: The transformation is a 180 - degree rotation about the vertex (let's say point E) that maps each point \((x,y)\) of the pre - image to a point \((-x + 2h,-y + 2k)\) where \((h,k)\) is the coordinates of the center of rotation (point E). If we take the center of rotation as \((0,0)\) (from the graph's symmetry), then \((x,y)\to(-x,-y)\).

Answer:

In words: The transformation is a 180 - degree rotation about the common vertex (the intersection point of the two triangles) of the pre - image and the image. Algebraically: If the center of rotation is \((h,k)\), the rule is \((x,y)\to(2h - x,2k - y)\). If we assume the center of rotation is the origin \((0,0)\), the rule is \((x,y)\to(-x,-y)\). (A more precise description can be given by identifying the exact center from the graph, but from the visual, 180 - degree rotation about the common vertex is the key transformation.)