Question

1. suppose the equation of line (ell) is (x = 1). given points (m(3,3)), (n(4,4)), and (o(5,2)), graph (\triangle mno) and the reflection image (r_{ell}(\triangle mno)). m(-1,3) n(-2,6) o(-3,2) 6. understand what is the reflection rule for the triangle and image with coordinates (a(2,4)), (b(4,6)), (c(5,2)), and (a(-4,-2)), (b(-6,-4)), (c(-2,-5))? reflection over the y axis 7. apply student a sits in a chair facing a mirror and sees the reflection image (b) of student b in the mirror. show th

Explanation:

Step1: Recall reflection formula

For a reflection over the line $x = a$, the formula for reflecting a point $(x,y)$ is $(2a - x,y)$. For the line $x = 1$, if we have a point $(x,y)$, its reflection is $(2\times1 - x,y)=(2 - x,y)$.
For point $M(3,3)$:
$x = 3,y = 3$, the reflected - point $M'$ has $x'=2 - 3=-1,y' = 3$, so $M'(-1,3)$.
For point $N(4,4)$:
$x = 4,y = 4$, the reflected - point $N'$ has $x'=2 - 4=-2,y' = 4$, so $N'(-2,4)$.
For point $O(5,2)$:
$x = 5,y = 2$, the reflected - point $O'$ has $x'=2 - 5=-3,y' = 2$, so $O'(-3,2)$.

Step2: Analyze reflection over y - axis

For a reflection over the y - axis, the rule is $(x,y)\to(-x,y)$.
Given $A(2,4)\to A'(-2,4)$ (should be $A'(-2,4)$ in the correct reflection over y - axis, the given $A'(-4,-2)$ in the problem has wrong coordinates for y - axis reflection), $B(4,6)\to B'(-4,6)$ (similarly wrong in the problem), $C(5,2)\to C'(-5,2)$ (wrong in the problem). The correct rule for reflection over the y - axis is that the x - coordinate changes sign and the y - coordinate remains the same.

Step3: Analyze mirror reflection concept

In a mirror reflection, the object and its image are at equal distances from the mirror line. If we consider the mirror as a line of reflection, and we know the position of point $A$ and the image $B'$ of point $B$, we can use the property of reflection. Let the mirror be a line. The mid - point of the line segment joining a point and its image lies on the mirror line. Also, the line joining a point and its image is perpendicular to the mirror line.

Answer:

For question 5, the reflected points of $M(3,3),N(4,4),O(5,2)$ over the line $x = 1$ are $M'(-1,3),N'(-2,4),O'(-3,2)$.
For question 6, the reflection rule for reflection over the y - axis is $(x,y)\to(-x,y)$.
For question 7, use the properties of mirror reflection such as equal distances from the mirror line and perpendicularity of the line joining the point and its image to the mirror line to analyze the positions of $A$, $B$ and $B'$.