Question

determining translations on the coordinate plane
what is the y - coordinate of point d after a translation of (x, y)→(x + 6, y - 4)?
d(3.5, )

Explanation:

Step1: Find original x - coordinate of D

From the translation rule $(x,y)\to(x + 6,y - 4)$ and the new x - coordinate of $D'$ which is $3.5$. We set up the equation $x+6 = 3.5$. Solving for $x$, we get $x=3.5 - 6=-2.5$. Looking at the graph, the original point $D$ has $x=-2.5$ and $y = 5$.

Step2: Apply y - translation

Use the y - translation part of the rule $y'=y - 4$. Substitute the original $y$ - value of point $D$ which is $y = 5$ into the formula. So $y'=5-4$.
$y' = 1$

Answer:

$1$