Question

what will be the new point location of point (5,-6) after a reflection over the y - axis and a translation 3 units up and 2 units right? wednesday - expressions and equations after solving the balance. write an equation for it. algebra balances. boxes that are the same size and shape must have the same number in them.

Explanation:

Step1: Reflect point over y - axis

The rule for reflecting a point $(x,y)$ over the y - axis is $(-x,y)$. Given the point $(5, - 6)$, after reflection over the y - axis, it becomes $(-5,-6)$.

Step2: Translate the reflected point

The rule for translation is $(x,y)\to(x + a,y + b)$, where $a$ is the horizontal translation and $b$ is the vertical translation. Here $a = 2$ (2 units right) and $b=3$ (3 units up). Starting with the point $(-5,-6)$, we have $x=-5$, $y = - 6$, $x'=-5 + 2=-3$, $y'=-6 + 3=-3$. So the new point is $(-3,-3)$.

Answer:

$(-3,-3)$