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 $3.5$. Let the original x - coordinate of $D$ be $x$. Then $x+6 = 3.5$, so $x=3.5 - 6=-2.5$. Looking at the graph, we can also visually estimate the original x - coordinate of $D$ is around $-2.5$. The original y - coordinate of $D$ is $5$.

Step2: Apply y - translation

The translation rule for the y - coordinate is $y\to y - 4$. The original y - coordinate of $D$ is $y = 5$. After translation, the new y - coordinate is $y_{new}=5-4$.
$y_{new}=1$

Answer:

$1$