Question

y(2,-4) is the image of y after a translation along the vector (-4,-3). what are the coordinates of y?
a (-1,6)
b (-6,-1)
c (6,-1)
d (1,6)

Explanation:

Step1: Understand the translation rule

A translation along the vector \((-4,-3)\) means \(x\) - coordinate is decreased by \(4\) and \(y\) - coordinate is decreased by \(3\). Let the original point \(Y\) have coordinates \((x,y)\). Then the image \(Y'\) has coordinates \((x - 4,y - 3)\).
We know \(Y'(2,-4)\), so we set up the equations:
\(x-4 = 2\) and \(y - 3=-4\)

Step2: Solve for \(x\)

For \(x-4 = 2\), add \(4\) to both sides of the equation:
\(x=2 + 4\)
\(x = 6\)

Step3: Solve for \(y\)

For \(y-3=-4\), add \(3\) to both sides of the equation:
\(y=-4 + 3\)
\(y=-1\)

Answer:

C. \((6,-1)\)