Question

1. a point r is at (4,-2). it is translated by (x,y)→(x - 5,y + 3), then reflected across the y - axis, and finally rotated 180 degrees about the origin. what are the new coordinates of r?

. a) (-1,-1)
. b) (1,1)
. c) (-1,1)
. d) (1,-1)
o a) (-1,-1)
o b) (1,1)
o c) (-1,1)
o d) (1,-1)

Explanation:

Step1: Apply the translation

The translation rule is $(x,y)\to(x - 5,y + 3)$. Given the point $R(4,-2)$, substitute $x = 4$ and $y=-2$ into the rule.
$x_1=4 - 5=-1$
$y_1=-2 + 3=1$
The point after translation is $(-1,1)$.

Step2: Apply the reflection across the y - axis

The rule for reflecting a point $(x,y)$ across the y - axis is $(x,y)\to(-x,y)$. For the point $(-1,1)$, we have $x=-1$ and $y = 1$.
$x_2=-(-1)=1$
$y_2=1$
The point after reflection is $(1,1)$.

Step3: Apply the 180 - degree rotation about the origin

The rule for rotating a point $(x,y)$ 180 degrees about the origin is $(x,y)\to(-x,-y)$. For the point $(1,1)$, we have $x = 1$ and $y = 1$.
$x_3=-1$
$y_3=-1$

Answer:

A. $(-1,-1)$