Question

i can describe the changes to the x - and y - coordinates of a figure after either dilation, translation, rotation or reflection. (8.g.a.3)

1. point a is located at coordinates (-4, 3)

a. rotate point a 180° using (0,0) as the center of rotation. plot and label your point b. what is the coordinate of point b?
b. translate point a two units to the right, then reflect across the x - axis. plot and label your point c. what is the coordinate of point c?
c. reflect point a across the y - axis, then translate two units to the right. plot and label your point d. what is the coordinate of point d?

Explanation:

Step1: Recall rotation rule

When rotating a point $(x,y)$ 180° about the origin $(0,0)$, the new coordinates $(x',y')$ are given by $x'=-x$ and $y'=-y$. For point $A(-4,3)$, $x = - 4$ and $y = 3$. So $x'=-(-4)=4$ and $y'=-3$. The coordinate of point $B$ is $(4,-3)$.

Step2: Recall translation - reflection rules

First, translate point $A(-4,3)$ two units to the right. The rule for translation to the right is $(x,y)\to(x + 2,y)$. So $A(-4,3)$ becomes $A_1(-4 + 2,3)=( - 2,3)$. Then reflect $A_1(-2,3)$ across the $x$-axis. The rule for reflection across the $x$-axis is $(x,y)\to(x,-y)$. So the coordinate of point $C$ is $(-2,-3)$.

Step3: Recall reflection - translation rules

First, reflect point $A(-4,3)$ across the $y$-axis. The rule for reflection across the $y$-axis is $(x,y)\to(-x,y)$. So $A(-4,3)$ becomes $A_2(4,3)$. Then translate $A_2(4,3)$ two units to the right. Using the rule $(x,y)\to(x + 2,y)$, the coordinate of point $D$ is $(4+2,3)=(6,3)$.

Answer:

a. $(4,-3)$
b. $(-2,-3)$
c. $(6,3)$