The slopes of four different lines are 3/5, -10/6, -5/3, and 9/15. do these lines determine a rectangle? explain why or why not

Question

The slopes of four different lines are 3/5, -10/6, -5/3, and 9/15. do these lines determine a rectangle? explain why or why not

Answer 1

3/5 = 9/15, so the lines with those slopes are parallel

-10/6 = -5/3, so the lines with those slopes are also parallel

3/5 and -5/3 are negative reciprocals of each other, so the lines with slopes 3/5 and 9/15 are perpendicular to the lines with slopes -5/3 and -10/6.

Yes, a rectangle is formed by these lines.

Answer 2

You need to have 2 perpendicular lines, which means the product of their slopes must be -1. The lines of slope 3/5 and -5/3 satisfy this. You also need a line parallel to the line of slope 3/5, and another line parallel to the line of slope -5/3. Parallel lines must have equal slopes. The line of slope -10/6=-5/3 is parallel to the line of slope -5/3, and the line of slope 9/15=3/5 is parallel to the line of slope 3/5. You have all the conditions to determine a rectangle.