Question

question 7
1 pts
what is the mapping for the reflection where △abc maps to △a′b′c?
(image of coordinate plane with triangle abc and its image abc)
options:
(x, y) → (-y, x)
(x, y) → (x, -y)
(x, y) → (-y, -x)
(x, y) → (-x, y)
question 8
1 pts
△stv has vertices s(-3, -2), t(-4, 3) and v(-2, 3). if (x, y) → (x - 2, y + 3), what are the vertices of its image?

Explanation:

Step1: Identify Coordinates

First, find coordinates of a point (e.g., A) and its image (A'). Let’s assume A has coordinates \((x, y)\) and A' has \((-x, y)\) (by observing the graph: if A is \((-a, b)\), A' is \((a, b)\), so \(x \to -x\), \(y\) remains).

Step2: Test Transformations

• Option 1: \((x,y)\to(-y,x)\) – Rotation (90°), not reflection. Eliminate.
• Option 2: \((x,y)\to(x,-y)\) – Reflection over x - axis. Doesn't match (y - coordinate same). Eliminate.
• Option 3: \((x,y)\to(-y,-x)\) – Rotation (180° + 90°), not reflection. Eliminate.
• Option 4: \((x,y)\to(-x,y)\) – Reflection over y - axis. Matches the coordinate change (x - coordinate flips sign, y stays).

Answer:

\((x, y) \to (-x, y)\) (the fourth option)