Question

if a translation of $(x,y)\to(x + 6,y - 10)$ is applied to figure abcd, what are the coordinates of $d$?
$(-5,-2)$
$(1,-12)$
$(4,-15)$
$(-9,-6)$

Explanation:

Step1: Find the coordinate of point D

From the graph, the coordinate of point \(D\) is \((-5,8)\).

Step2: Apply the translation rule

The translation rule is \((x,y)\to(x + 6,y-10)\).
For \(x=-5\), \(x+6=-5 + 6=1\).
For \(y = 8\), \(y-10=8-10=-2\).

Answer:

\((1,-2)\)

It seems there is a mistake in the provided options. If we assume the coordinate of \(D\) is \((-5, - 2)\) (maybe a mis - read of the graph):

Step1: Apply the translation rule

The translation rule is \((x,y)\to(x + 6,y-10)\).
For \(x=-5\), \(x + 6=-5+6 = 1\).
For \(y=-2\), \(y-10=-2-10=-12\).