Question

point g is located at (5, -2). determine the coordinates of the image after each transformation. a 180° rotation around the origin. a translation 2 units to the left and 1 unit up.

Explanation:

Step1: Apply 180 - degree rotation rule

For a 180 - degree rotation around the origin, the rule is $(x,y)\to(-x,-y)$. Given point $G(5, - 2)$, we substitute $x = 5$ and $y=-2$ into the rule.
$x'=-5,y' = 2$

Step2: Apply translation rule

The translation rule for 2 units to the left and 1 unit up is $(x,y)\to(x - 2,y + 1)$. Starting with the point after rotation $(-5,2)$, we substitute $x=-5$ and $y = 2$ into the translation rule.
$x''=-5-2=-7,y''=2 + 1=3$

Answer:

Coordinates after 180 - degree rotation: $(-5,2)$
Coordinates after translation: $(-7,3)$