Question

1. quadrilateral abcd and its image, abcd, are shown on the coordinate grid below. which rule best describes the transformation that was used to form quadrilateral abcd? a) (x, y)→(−y, x) b) (x, y)→(x, −y) c) (x, y)→(y, x) d) (x, y)→(−y, −x) 5) which 2 figures do not have a horizontal line of symmetry? a) b) c) d)

Explanation:

4)

Step1: Check transformation rule for a point

Take a point from quadrilateral \(ABCD\), say \(A(0, 6)\). Its image \(A'(- 6,0)\) in \(A'B'C'D'\).

Step2: Analyze transformation rules

For option a) \((x,y)\to(-y,x)\), if \(x = 0\) and \(y=6\), then \((0,6)\to(-6,0)\). Checking other points also satisfies this rule.

Step1: Define horizontal - line of symmetry

A horizontal line of symmetry divides a figure into two congruent parts such that one part is the mirror - image of the other with respect to a horizontal line.

Step2: Analyze each figure

• Figure a) (yin - yang symbol): It has no horizontal line of symmetry.
• Figure b) (wheel - like figure): It has horizontal line of symmetry.
• Figure c) (figure with loops): It has horizontal line of symmetry.
• Figure d) (equilateral triangle): It has no horizontal line of symmetry.

Answer:

a) \((x,y)\to(-y,x)\)

5)