Question

which representation of a transformation on a coordinate grid does not preserve congruence? (a) $(x,y)\to(\frac{1}{7}x,\frac{1}{7}y)$ (b) $(x,y)\to(x + 7,y + 7)$ (c) $(x,y)\to(x,-y)$ (d) $(x,y)\to(y,-x)$

Explanation:

Step1: Recall congruence - preserving transformations

Rigid transformations (translations, rotations, reflections) preserve congruence.

• Translation: \((x,y)\to(x + a,y + b)\) (Option B is a translation).
• Reflection: \((x,y)\to(x,-y)\) (Option C is a reflection over the \(x -\)axis).
• Rotation: \((x,y)\to(y,-x)\) is a \(270^{\circ}\) counter - clockwise rotation (Option D is a rotation).

Step2: Analyze non - rigid transformation

A dilation \((x,y)\to(kx,ky)\) (\(k
eq1\)) changes the size of the figure. For \((x,y)\to(\frac{1}{7}x,\frac{1}{7}y)\) (\(k = \frac{1}{7}
eq1\)), it is a dilation.

Answer:

A. \((x,y)\to(\frac{1}{7}x,\frac{1}{7}y)\)