Question

sandbox aliyah is drawing the top view of a square sandbox on a coordinate plane with vertices at d(1, 1), e(1, 6), f(6, 6), and g(6, 1). she wants to change the location of the sandbox so that it is in the shade. she reflects the sandbox in the line ( x = 1 ). find the coordinates of the image of the sandbox

Explanation:

Step1: Recall reflection rule for $x=1$

For a point $(x,y)$, reflection over $x=1$ uses:
$$x' = 2(1) - x, \quad y' = y$$

Step2: Calculate $D'$ coordinates

Substitute $D(1,1)$:
$$x' = 2(1)-1=1, \quad y'=1$$

Step3: Calculate $E'$ coordinates

Substitute $E(1,6)$:
$$x' = 2(1)-1=1, \quad y'=6$$

Step4: Calculate $F'$ coordinates

Substitute $F(6,6)$:
$$x' = 2(1)-6=-4, \quad y'=6$$

Step5: Calculate $G'$ coordinates

Substitute $G(6,1)$:
$$x' = 2(1)-6=-4, \quad y'=1$$

Answer:

$D'(1, 1)$
$E'(1, 6)$
$F'(-4, 6)$
$G'(-4, 1)$