Question

a point at (1,3) is reflected across the y - axis, then translated by the rule (x,y)→(x - 2,y + 4), and finally rotated 90° counterclockwise about the origin. what is the location of the final image?
a) (7, - 3)
b) (3, - 5)
c) (-7,3)
d) (-3,5)
a) (7, - 3)
b) (3, - 5)
c) (-7,3)
d) (-3,5)

Explanation:

Step1: Reflect across y - axis

The rule for reflecting a point $(x,y)$ across the y - axis is $(x,y)\to(-x,y)$. Given the point $(1,3)$, after reflection across the y - axis, it becomes $(-1,3)$.

Step2: Apply the translation rule

The translation rule is $(x,y)\to(x - 2,y + 4)$. Substitute $x=-1$ and $y = 3$ into the rule. We get $x=-1-2=-3$ and $y=3 + 4=7$. So the point after translation is $(-3,7)$.

Step3: Rotate 90 - counterclockwise about the origin

The rule for rotating a point $(x,y)$ 90 degrees counter - clockwise about the origin is $(x,y)\to(-y,x)$. Substitute $x=-3$ and $y = 7$ into the rule. We get $x=-7$ and $y=-3$. So the final point is $(-7,-3)$.

Answer:

None of the given options are correct. The correct answer should be $(-7,-3)$.