Question

question 16
5 pts
a point (0, 6) is translated 2 units left and then rotated 180 degrees about the origin. what are the coordinates of the final image?
(-2, -6)
(2, 6)
(-2, 6)
(2, -6)
what is the result of reflecting the point (-5, 7) over the x - axis and then translating it 3 units left?
(-2, 7)
(-8, 7)
(-8, -7)
(-2, -7)

Explanation:

Step1: Perform the translation

For a point $(x,y)$ translated $a$ units left, the new - $x$ coordinate is $x - a$. Given the point $(0,6)$ translated 2 units left, the new point after translation is $(0 - 2,6)=(-2,6)$.

Step2: Perform the rotation

The rule for rotating a point $(x,y)$ 180 degrees about the origin is $(x,y)\to(-x,-y)$. For the point $(-2,6)$ rotated 180 degrees about the origin, we have $(-(-2),-6)=(2, - 6)$.

Answer:

$(2,-6)$