Question

question 2: reflect each shape in the mirror line given: (a) (b) (c) (d) (e) (f) question 3: (a) reflect shape a in the line x = 1 (b) reflect shape b in the line x = -2 (c) reflect shape c in the line y = -1 (d) reflect shape d in the line y = 2 (e) reflect shape e in the line x = -1 (f) reflect shape f in the line y = 3

Explanation:

Step1: Recall reflection rules

For reflection over a vertical line $x = a$, the $x$-coordinate of a point $(x,y)$ changes as $x'=2a - x$ and the $y$-coordinate remains the same $y'=y$. For reflection over a horizontal line $y = b$, the $y$-coordinate of a point $(x,y)$ changes as $y'=2b - y$ and the $x$-coordinate remains the same $x'=x$.

Step2: For Question 2

For each shape, measure the perpendicular distance of each vertex from the mirror - line. Then, on the opposite side of the mirror - line, mark a point at the same perpendicular distance from the mirror - line. Connect the new vertices to get the reflected shape.

Step3: For Question 3 (a)

For shape A reflected in the line $x = 1$, if a vertex of shape A has coordinates $(x,y)$, the new $x$-coordinate of the reflected vertex is $x'=2\times1 - x=2 - x$ and $y' = y$. Do this for all vertices of shape A and connect them.

Step4: For Question 3 (b)

For shape B reflected in the line $x=-2$, if a vertex of shape B has coordinates $(x,y)$, the new $x$-coordinate of the reflected vertex is $x'=2\times(-2)-x=-4 - x$ and $y' = y$. Do this for all vertices of shape B and connect them.

Step5: For Question 3 (c)

For shape C reflected in the line $y = - 1$, if a vertex of shape C has coordinates $(x,y)$, the new $y$-coordinate of the reflected vertex is $y'=2\times(-1)-y=-2 - y$ and $x' = x$. Do this for all vertices of shape C and connect them.

Step6: For Question 3 (d)

For shape D reflected in the line $y = 2$, if a vertex of shape D has coordinates $(x,y)$, the new $y$-coordinate of the reflected vertex is $y'=2\times2 - y=4 - y$ and $x' = x$. Do this for all vertices of shape D and connect them.

Step7: For Question 3 (e)

For shape E reflected in the line $x=-1$, if a vertex of shape E has coordinates $(x,y)$, the new $x$-coordinate of the reflected vertex is $x'=2\times(-1)-x=-2 - x$ and $y' = y$. Do this for all vertices of shape E and connect them.

Step8: For Question 3 (f)

For shape F reflected in the line $y = 3$, if a vertex of shape F has coordinates $(x,y)$, the new $y$-coordinate of the reflected vertex is $y'=2\times3 - y=6 - y$ and $x' = x$. Do this for all vertices of shape F and connect them.

Answer:

The reflected shapes for Question 2 and Question 3 should be drawn on the respective grids following the above - described rules for reflection. Since this is a graphical problem, the actual answer is the set of correctly drawn reflected shapes on the given grids.