Question

Use a graph paper. Plot \[A\left( { - 4,2} \right){\text{, }}B{\text{ }}\left( { - 6,0} \right),\] reflect A in the x -axis, the y-axis and the origin to form resp. Reflect B in the y- axis to form $B'$. Join all the points to obtain a geometric figure Name the figure, and write the equation of the line that divides it into equal halves.

Answer 1

Hint: Reflecting the point means the same point on the opposite side of the axis.
First, we are going to plot the given two points \[A\left( { - 4,2} \right){\text{, }}B{\text{ }}\left( { - 6,0} \right),\] then on reflecting the point A on x-axis and y-axis, we get them as , then on reflecting B, we get $B'(6,0)$. Then we are going to join all the points and then find the equations which divide the formed figure into two equal halves.

Complete step by step answer:
First, we are going to mark the given two points onto the graph paper, then we get

Then after reflecting the point A on x-axis and y-axis, we get them as, then on reflecting B, we get $B'(6,0)$.

Then we are going to join all the given points and form a figure. Which is

From the figure, it is understandable that the figure formed is a hexagon, and the equations which divide the figure into two equal halves are
$x = 0\,\,\& \,\,y = 0$

Note: Reflection means plotting a point that has the same distance from the origin that to the distance of the actual point from the origin. Also, the equations divide lie on x-axis and y-axis because of the points being reflected onto the either sides and the both axis being the mid points of the figure formed.