Question

1. draw the image of figure rstu after a translation 3 units left and 4 units down and a reflection across the y - axis.

Explanation:

Step1: Identify original coordinates

Original vertices: $R(1,4)$, $S(1,2)$, $T(0,2)$, $U(-1,4)$

Step2: Apply translation (3 left, 4 down)

Translation rule: $(x,y)\to(x-3,y-4)$
$R'(1-3,4-4)=(-2,0)$
$S'(1-3,2-4)=(-2,-2)$
$T'(0-3,2-4)=(-3,-2)$
$U'(-1-3,4-4)=(-4,0)$

Step3: Reflect across y-axis

Reflection rule: $(x,y)\to(-x,y)$
$R''(-(-2),0)=(2,0)$
$S''(-(-2),-2)=(2,-2)$
$T''(-(-3),-2)=(3,-2)$
$U''(-(-4),0)=(4,0)$

Step4: Plot final vertices

Plot $R''(2,0)$, $S''(2,-2)$, $T''(3,-2)$, $U''(4,0)$ and connect them.

Answer:

The final image has vertices at $(2,0)$, $(2,-2)$, $(3,-2)$, and $(4,0)$. When plotted and connected, this forms the translated and reflected quadrilateral $R''S''T''U''$.