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 coordinates of point c?

Explanation:

Step1: Recall rotation rule

When rotating a point $(x,y)$ 180° about the origin $(0,0)$, the new - coordinates are $(-x,-y)$. Point A has coordinates $(4,3)$. So for point B (after 180° rotation of A about the origin), we have $x = 4$ and $y = 3$. The new coordinates of B are $(-4,-3)$.

Step2: Recall translation and reflection rules

First, translate point A two units to the right. The rule for translation to the right is $(x,y)\to(x + 2,y)$. For point A$(4,3)$, after translation, the new point (let's call it A') has coordinates $(4 + 2,3)=(6,3)$. Then, reflect A' across the x - axis. The rule for reflection across the x - axis is $(x,y)\to(x,-y)$. So for point A'$(6,3)$, the coordinates of point C are $(6,-3)$.

Answer:

a. The coordinates of point B are $(-4,-3)$.
b. The coordinates of point C are $(6,-3)$.