Question

triangle klm and triangle klm are shown on the coordinate plane. write the rule describes the composition of transformations that maps triangle klm to triangle klm. enter your answers in the boxes. r0,□°t(□,□)(x,y)

Explanation:

Step1: Identify transformation type

First, observe the orientation change. Triangle KLM is rotated 180° about the origin. The rule for a 180 - degree rotation about the origin is $(x,y)\to(-x,-y)$.

Step2: Identify translation

After rotation, the triangle is translated. Comparing the coordinates of corresponding points after rotation and the final image K''L''M'', we see that it is translated 1 unit to the left and 2 units down. The rule for translation 1 unit left and 2 units down is $(x,y)\to(x - 1,y - 2)$.
Combining the rotation and translation, the composition of transformations has the rule: First rotate 180° about the origin $(x,y)\to(-x,-y)$ and then translate 1 unit left and 2 units down $(-x,-y)\to(-x - 1,-y - 2)$.

Answer:

$180$, $(-1,-2)$