Math CentralQuandaries & Queries


Question from christianah, a student:

Two parallel lines have the equations y=x+4 and y=x-2.Two additional lines are drawn to form a square.What is the side length of the square?Write possible equations for the additional lines. Explain and justify your reasoning.


I can help get you started. First I sketched a graph of the two given lines.


Let P be the point where the line y = x + 4 intersects the Y-axis.

What are the coordinates of P?

Draw the line through P that is perpendicular to y = x + 4. This is going to form the third side of the square. It intersects y = x - 2 at Q. The line y = x + 4 has slope 1.

What is the slope of the line through P and Q?
What is the equation of this line?
What are the coordinates of Q?

The side length of the square is the distance from P to Q. You can find this using the distance formula or by using Pythagoras theorem directly.

I hope this helps. Write back if you need more assistance.


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