Before you get to that, what does it mean for the points to be symmetric about y = mx + b?RTCNTC said:Determine values for m and b so that the points (8, 2) and (4, 8) are symmetric about the line y = mx + b.
Do I plug the coordinates of each point into the formula
y = mx + b individually to find values for m and b?
Absolutely NOT! That would give you the equation of the line that contains (8, 2) and (4, 6) but these two points do NOT lie on the line you seek! They are symmetric about that line. In particular, the line you seek must be the perpendicular bisector of the line segment between (8, 2) and (4, 8).RTCNTC said:Determine values for m and b so that the points (8, 2) and (4, 8) are symmetric about the line y = mx + b.
Do I plug the coordinates of each point into the formula
y = mx + b individually to find values for m and b?
HallsofIvy said:Absolutely NOT! That would give you the equation of the line that contains (8, 2) and (4, 6) but these two points do NOT lie on the line you seek! They are symmetric about that line. In particular, the line you seek must be the perpendicular bisector of the line segment between (8, 2) and (4, 8).
What are the coordinates of the point midway between (8, 2) and (4, 6)? What is the slope of the line through (8, 2) and (4, 6)? What is the slope of a line perpendicular to that line? Finally, what is the equation of the line through that midpoint perpendicular to that line?