Answer:
B
Step-by-step explanation:
Consider all options:
A. Transformation with the rule
[tex](x,y)\rightarrow (x,-y)[/tex]
is a reflection across the x-axis.
Reflection across the x-axis preserves the congruence.
B. Transformation with the rule
[tex](x,y)\rightarrow \left(\dfrac{7}{8}x,\dfrac{7}{8}y\right)[/tex]
is a dilation with a scale factor of [tex]\frac{7}{8}[/tex] over the origin.
Dilation does not preserve the congruence as you get smaller figure.
C. Transformation with the rule
[tex](x,y)\rightarrow (x+6,y-4)[/tex]
is a translation 6 units to the right and 4 units down.
Translation 6 units to the right and 4 units down preserves the congruence.
D. Transformation with the rule
[tex](x,y)\rightarrow (y,-x)[/tex]
is a clockwise rotation by [tex]90^{\circ}[/tex] angle over the origin.
Clockwise rotation by [tex]90^{\circ}[/tex] angle over the origin preserves the congruence.
