Question

The point (3,-5) is successively reflected across the x-axis, 1 point then y-axis and then x-axis again. The rectangle formed by these 4 points is dilated by a factor of 2. What is the perimeter of the newly dilated rectangle?

Answer 1

To answer this questions we have to remember the formula for the relfection across the axis.

A reflection across the x-axis is given by:

`(x,y)\rightarrow(x,-y)`

A relfection across the y-axis is given by:

`(x,y)\rightarrow(-x,y)`

With this in mind let's find the vertex of our rectangle.

The first vertex is the point (3,-5)

The second vertex is obtained by reflecting the first one acroos the x-axis:

`(3,-5)\rightarrow(3,5)`

Then, the second vertex is (3,5).

The third vertex is obtained by reflecting the second one across the y-axis:

`(3,5)\rightarrow(-3,5)`

Then, the third vertex is (-3,5).

Finally, the last vertex is obtained by reflecting the third one across the x-axis:

`(-3,5)\rightarrow(-3,-5)`

Therefore, the vertexes of our rectangle are (3,-5) (3,5) (-3,5) and (-3,-5).

To have a better understanding of the problem let's plot them in the plane

From the graph we notice that the length of the rectangle is 10 and the width is 6. We know that the perimeter of a rectangle is:

`P=2l+2w`

Then, we have:

`P=2(10)+2(6)=20+12=32`

Therefore, the perimeter of the rectangle is 32 units.