Question

unit 2, lesson 9: describing transformations in the coordinate plane
warm - up: math talk: transforming a point
mentally find the coordinates of the image of a under each transformation
a=(3,2)
translate a by the directed line segment from (0,0) to (0,2)
translate a by the directed line segment from (0,0) to (-4,0)
reflect a across the y - axis
rotate a 180 degrees clockwise using the origin as a center.

Explanation:

Step1: Recall translation rule for vertical shift

When translating a point $(x,y)$ by the directed - line segment from $(0,0)$ to $(0,2)$, we add 2 to the $y$ - coordinate. Given $A=(3,2)$, the new point is $(3,2 + 2)=(3,4)$.

Step2: Recall translation rule for horizontal shift

When translating a point $(x,y)$ by the directed - line segment from $(0,0)$ to $(-4,0)$, we subtract 4 from the $x$ - coordinate. Given $A=(3,2)$, the new point is $(3-4,2)=(-1,2)$.

Step3: Recall reflection rule across y - axis

When reflecting a point $(x,y)$ across the $y$ - axis, the $x$ - coordinate changes sign. Given $A=(3,2)$, the new point is $(-3,2)$.

Step4: Recall rotation rule for 180 - degree clockwise rotation

When rotating a point $(x,y)$ 180 degrees clockwise about the origin, the new coordinates are $(-x,-y)$. Given $A=(3,2)$, the new point is $(-3,-2)$.

Answer:

1. Translation by directed line segment from $(0,0)$ to $(0,2)$: $(3,4)$
2. Translation by directed line segment from $(0,0)$ to $(-4,0)$: $(-1,2)$
3. Reflection across the $y$ - axis: $(-3,2)$
4. 180 - degree clockwise rotation about the origin: $(-3,-2)$