Question

One line divides a plane into two regions. Two lines can divide a plane into at most four regions. What is the maximum number of regions possible using eight lines? Hint: Draw a picture. Keep adding lines. Count the regions you have each time. Do you see a parttern in your results?

Please answer it step-by-step.

Answer 1

The maximum number of regions possible using eight lines will be 64 regions.

How to get the value?

From the information given, one line divides a plane into two regions, two lines can divide a plane into at most four regions. The relationship her is that the square of the number is given.

Therefore, the number of regions will be:

= 8²

= 8 × 8

= 64 regions

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