Question

find a translation that has the same effect as the composition of translations below.
$t_{\langle 2,5 \
angle}(x,y)$ followed by $t_{\langle -5,9 \
angle}(x,y)$
choose the correct answer below.
\\(\bigcirc\\) a. \\((x,y)\to(x - 3,y + 14)\\)
\\(\bigcirc\\) b. \\((x,y)\to(x - 3,y - 4)\\)
\\(\bigcirc\\) c. \\((x,y)\to(x + 7,y + 14)\\)
\\(\bigcirc\\) d. \\((x,y)\to(x + 7,y - 4)\\)

Explanation:

Step1: Define first translation

$T_{\langle 2,5
angle}(x,y) = (x+2, y+5)$

Step2: Apply second translation

$T_{\langle -5,9
angle}(x+2, y+5) = (x+2-5, y+5+9)$

Step3: Simplify coordinates

$(x-3, y+14)$

Answer:

A. (x,y)→(x−3,y+14)