Question

△abc is mapped to △abc using each of the given rules. which rules would result in △abc being congruent to or not congruent to △abc? drag and drop each rule into the boxes to correctly classify it as congruent or not congruent. (x, y)→(x + 3, y - 4) (x, y)→(3x, 3y) (x, y)→(0.4x, 0.4y) (x, y)→(x/3, y/3) (x, y)→(-x, -y)

Explanation:

Step1: Recall congruence rules

Rigid - motions (translations, rotations, reflections) preserve congruence. Dilations change the size and do not preserve congruence.

Step2: Analyze $(x,y)\to(x + 3,y - 4)$

This is a translation. Translations are rigid - motions. So, the triangles are congruent.

Step3: Analyze $(x,y)\to(3x,3y)$

This is a dilation with a scale factor of 3. Dilations change the size of the figure, so the triangles are not congruent.

Step4: Analyze $(x,y)\to(0.4x,0.4y)$

This is a dilation with a scale factor of 0.4. Dilations change the size of the figure, so the triangles are not congruent.

Step5: Analyze $(x,y)\to(\frac{x}{3},\frac{y}{3})$

This is a dilation with a scale factor of $\frac{1}{3}$. Dilations change the size of the figure, so the triangles are not congruent.

Step6: Analyze $(x,y)\to(-x,-y)$

This is a rotation of 180° about the origin. Rotations are rigid - motions. So, the triangles are congruent.

Answer:

Congruent: $(x,y)\to(x + 3,y - 4)$, $(x,y)\to(-x,-y)$
Not Congruent: $(x,y)\to(3x,3y)$, $(x,y)\to(0.4x,0.4y)$, $(x,y)\to(\frac{x}{3},\frac{y}{3})$