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Math challenge II geometry 3.18

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Math challenge II geometry 3.18
by Jialin Wang - Wednesday, September 22, 2021, 8:10 PM

Hi, I have a question about 3.18.

The line given by x42=y513x−42=y−513 goes through points A=(4,5)A=(4,5) and BB. What is yByB?

This question is ambiguous. Since it's a linear function, then there are infinite other possible points. B could be anything on this line. There is no x or y coordinates given for B so B could by anything on the line

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Re: Math challenge II geometry 3.18
by Dr. Kevin Wang - Friday, September 24, 2021, 5:39 PM

You are right, the question is not given correctly.  For the point $B$, the intended coordinates are $(2, y_B)$ , and we want to find out $y_B$.

Here is the corrected question:

The line given by $\displaystyle \frac{x - 4}{2} = \frac{y - 5}{13}$ goes through point $B = (2, y_B)$. What is $y_B$?