Question

Which representation of a transformation on a coordinate grid does not preserve congruence?

Answer 1

Answer:

B

Step-by-step explanation:

Consider all options:

A. Transformation with the rule

$(x,y)\rightarrow (x,-y)$

is a reflection across the x-axis.

Reflection across the x-axis preserves the congruence.

B. Transformation with the rule

$(x,y)\rightarrow \left(\dfrac{7}{8}x,\dfrac{7}{8}y\right)$

is a dilation with a scale factor of $\frac{7}{8}$ over the origin.

Dilation does not preserve the congruence as you get smaller figure.

C. Transformation with the rule

$(x,y)\rightarrow (x+6,y-4)$

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

$(x,y)\rightarrow (y,-x)$

is a clockwise rotation by $90^{\circ}$ angle over the origin.

Clockwise rotation by $90^{\circ}$ angle over the origin preserves the congruence.