Question

which process will transform figure h onto figure k?reflect figure h over the x-axis, followed by a reflection over the y-axis.rotate figure h $180^{\circ}$ about the origin.rotate figure h $180^{\circ}$ about the origin, then translate 2 units to the left.reflect figure h over the x-axis, followed by a translation of 2 units to the left, followed by a reflection over the y-axis.

Explanation:

First, identify vertices of Figure H: let's take the three vertices as $(2,1)$, $(6,1)$, $(4,3)$.

Step1: Rotate 180° about origin

Rotation rule: $(x,y)\to(-x,-y)$.
New points: $(-2,-1)$, $(-6,-1)$, $(-4,-3)$.

Step2: Translate 2 units left

Translation rule: $(x,y)\to(x-2,y)$.
New points: $(-4,-1)$, $(-8,-1)$, $(-6,-3)$.

Step3: Match to Figure K

These points match the vertices of Figure K (blue triangle). Verify other options fail:

• Reflect x then y axis: $(x,y)\to(-x,-y)$ (no translation, doesn't match).
• Rotate 180° only: gives $(-2,-1), (-6,-1), (-4,-3)$ (no left shift, doesn't match).
• Reflect x then translate then reflect y: $(x,y)\to(-(x-2),-y)$ gives $(-0,-1), (-4,-1), (-2,-3)$ (doesn't match).

Answer:

Rotate Figure $H$ $180^\circ$ about the origin, then translate 2 units to the left.