Question

question 17 (5 points)
rectangle efgh is reflected across the origin and then rotated 90° clockwise about the origin, forming rectangle efgh. what are the coordinates of rectangle efgh?
a) e(-1, 5), f(-1, 1), g(-4, 1), h(-4, 5)
b) e(1, -5), f(1, -1), g(4, -1), h(4, -5)
c) e(5, 1), f(1, 1), g(1, 4), h(5, 4)
d) e(-1, -5), f(-1, -1), g(-4, -1), h(-4, -5)

Explanation:

Step1: Identify original coordinates

From the graph: $E(-5, -1)$, $F(-1, -1)$, $G(-1, -4)$, $H(-5, -4)$

Step2: Reflect across origin

Rule: $(x,y)\to(-x,-y)$
$E' = (5, 1)$, $F' = (1, 1)$, $G' = (1, 4)$, $H' = (5, 4)$

Step3: Rotate 90° clockwise about origin

Rule: $(x,y)\to(y,-x)$
$E'' = (1, -5)\to(-1, 5)$
$F'' = (1, -1)\to(-1, 1)$
$G'' = (4, -1)\to(-4, 1)$
$H'' = (4, -5)\to(-4, 5)$

Answer:

A) $E''(-1, 5), F''(-1, 1), G''(-4, 1), H''(-4, 5)$