Question

select the correct descriptions that transformed △abc into △a b c. reflection across y = x 270° clockwise rotation 90° clockwise rotation translation (x - 5, y + 1)

Explanation:

Step1: Recall transformation rules

For reflection across $y = x$, $(x,y)\to(y,x)$. For rotation, $90^{\circ}$ clock - wise rotation: $(x,y)\to(y, - x)$; $270^{\circ}$ clock - wise rotation: $(x,y)\to(-y,x)$. For translation $(x - 5,y + 1)$, $(x,y)\to(x - 5,y + 1)$.

Step2: Analyze point coordinates

Let's assume $A=(3,2)$, $B=(4,5)$, $C=(7,1)$. After applying translation $(x - 5,y + 1)$:
$A=(3,2)\to A'=(3 - 5,2 + 1)=(-2,3)$
$B=(4,5)\to B'=(4 - 5,5 + 1)=(-1,6)$
$C=(7,1)\to C'=(7 - 5,1 + 1)=(2,2)$ which matches the graph.
For reflection across $y = x$, $A=(3,2)\to(2,3)
eq A'$. For $90^{\circ}$ clock - wise rotation, $A=(3,2)\to(2,-3)
eq A'$. For $270^{\circ}$ clock - wise rotation, $A=(3,2)\to(-2,3)$ but checking other points doesn't match overall.

Answer:

translation (x - 5, y + 1)