**The Prompt**

**Given:**The green, red and blue points are collinear. What is the dimension of the blue square if the green and red squares are 4x4 and 7x7 respectively?

After a few minutes, B comes up and says, "Mr. Cox, can you check this out. I think I've got something."

She shows me her diagram.

And her results.

Yep, kid. You've got something.

## 4 comments:

I am stealing that question. I don't think I will give the (0,4) coordinate and simply ask what they can tell me about the three squares.

Awesome question! Interesting comment above. I think the "openness" of the question would depend on the ability of the students. Personally, I would give this question to a year 9 or year 10 group and would keep it the way it is. The co-ordinates possibly act as a clue as to how a student might go about solving this. Depending on the ability, I would think about taking the co-ordinates out.

I know this post is 10 years old, but I believe the formula for N is incorrect. Shouldn't it be n=[(m^2 - k^2)/k]+k? I substituted k+m as the x and n as the y along with (m-k)/k as the slope into y=mx+b and simplified. I'm not certain how you achieved your formula for n. Great problem though that I'm presenting to my advanced-level 8th graders!

re: last comment 8.Nov.22. If you set the two formulas for n equal to each other (assume truth of both, try to verify if accurate), you get

m(m-k)/k + m = (m^2 - k^2)/k + k. Multiply by k on both sides and distribute, you get m^2 - km + km = m^2 - k^2 + k^2. This simplifies to 0 = 0, so they are equivalent equations. I also don't exactly know how the original formula came to be, but it doesn't contradict yours.

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