A rectangle has area 64 cm^2. A straight line is to be drawn from one corner of the rectangle to the midpoint of one of the two more distant sides. What is the minimum possible length of such a line

The minimum possible length of such a line is 8 cm

Step-by-step explanation:

If we had a rectangle, we can name each side "a" and "b".

The area of the rectangle will be:

Note: This is the constraint of our optimiztion problem.

Applying the Pitagoras theorem, the line, as in the figure attached, will have a length of:

We can replace "a" as a function of "b":

Then,

To calculate the minimum length, we derive and equal to zero:

Now, we know that one side is 5.66 cm.

Then, the other side should be:

The length of the line for this side dimensions will be:

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.

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step-by-step explanation: