Question

lesson 6 practice problems problem 1 draw polygon a in the coordinate plane. a. draw polygon b, the image of a, using the y - axis as the line of reflection. b. draw polygon c, the image of b, using the x - axis as the line of reflection. c. draw polygon d, the image of c, using the x - axis as the line of reflection. problem 2 the point (-4,1) is rotated 180 degrees counterclockwise using center (-3,0). what are the coordinates of the image? a. (-5,-2) b. (-4,-1) c. (-2,-1) d. (4,-1)

Explanation:

Step1: Find the translation vector from rotation center

To rotate a point $(x_1,y_1)$ 180 - degrees counter - clockwise about a center $(x_0,y_0)$, first find the vector from the center of rotation to the point. The vector from $(-3,0)$ to $(-4,1)$ is $(-4-(-3),1 - 0)=(-1,1)$.

Step2: Reverse the vector for 180 - degree rotation

For a 180 - degree counter - clockwise rotation, we reverse the components of the vector. So the new vector is $(1,-1)$.

Step3: Find the coordinates of the rotated point

Add the new vector to the center of rotation $(-3,0)$. The new $x$ - coordinate is $-3 + 1=-2$, and the new $y$ - coordinate is $0+( - 1)=-1$.

Answer:

C. $(-2,-1)$