Using a graph Paper, plot the points \[A(6,4)\] and \[B(0,4)\] .
A. Reflects A and B in the origin to get the images A’ and B’ .
B. Write the coordinates of A’ and B’ .
C. State the geometrical name of the figure ABA’B’ .
D. Find its Perimeter.

Hint: In a point reflection in the origin, the image of the point (x,y) is the point (-x,-y). We will use this to get the points of A’ and B’ then we will join the lines to see which figure is coming forth.

Complete step by step answer:
A.

From the Figure and the Hint it is clear that
B. Coordinates of A’ is (-6, -4) and B’ is (0,-4)
C. Also from the figure it is clear that the figure AB A'B’ is actually a parallelogram
D. In the triangle .’ BOO’
\[\begin{array}{l}
OO' = 3units\\
OB = 4units
\end{array}\]
Therefore by pythagoras theorem we will get it as
\[\begin{array}{l}
BO' = \sqrt {O{B^2} + O'{O^2}} \\
 \Rightarrow BO' = \sqrt {{4^2} + {3^2}} \\
 \Rightarrow BO' = \sqrt {25} \\
 \Rightarrow BO' = 5units
\end{array}\]
Since BO’ is 5 units
\[BA' = AB = 10 units\]
Which means that the perimeter of ABA’B’ \[ = (6 + 10 + 6 + 10)units = 32units\]

Note: Remember that The reflection of the point (x,y) across the x-axis is the point (x,-y), The reflection of the point (x,y) across the y-axis is the point (-x,y) and In a point reflection in the origin, the image of the point (x,y) is the point (-x,-y).