Question

consider the translation ((x,y)\to(x + 3,y - 2)). for each of the following, draw the image of the figure under the translation and find the coordinates of the images of the labeled points. \
b) for triangle (abc), type the image of each vertex. \
(a(-4,2)\to a) (type an ordered pair.) \
(b(1,5)\to b) (type an ordered pair.) \
(c(2,-1)\to c) (type an ordered pair.)

Explanation:

Step1: Apply the translation rule to \(x\) - coordinate

The translation rule is \((x,y)\to(x + 3,y-7)\). For the \(x\) - coordinate of a point \((x,y)\), we add \(3\) to the original \(x\) - value.

Step2: Apply the translation rule to \(y\) - coordinate

For the \(y\) - coordinate of a point \((x,y)\), we subtract \(7\) from the original \(y\) - value.

For point \(C(2,-1)\):

• The new \(x\) - coordinate is \(x'=2 + 3=5\)
• The new \(y\) - coordinate is \(y'=-1-7=-8\)

Answer:

\(C'(5,-8)\)