Question

the coordinates of the vertices of \\( \triangle abc \\) are \\( a(-5,2) \\), \\( b(-2,4) \\), and \\( c(-4,7) \\). what are the coordinates of the image of \\( a \\) after the translation \\( (x,y)\to(x + 6,y - 5) \\)?
a \\( (-10,8) \\)
b \\( (-2,4) \\)
c \\( (-3,1) \\)
d \\( (1,-3) \\)

Explanation:

Step1: Calculate the new x - coordinate

For the translation \((x,y)\to(x + 6,y-5)\), given \(x=-5\) (from point \(A(-5,2)\)), the new \(x\) - coordinate is \(x+6=-5 + 6\).
\(x+6=1\)

Step2: Calculate the new y - coordinate

Given \(y = 2\) (from point \(A(-5,2)\)), the new \(y\) - coordinate is \(y-5=2-5\).
\(y - 5=-3\)

Answer:

D. \((1,-3)\)