MHB Finding Values for m and b to Create a Symmetric Line

  • Thread starter Thread starter mathdad
  • Start date Start date
mathdad
Messages
1,280
Reaction score
0
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?
 
Mathematics news on Phys.org
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?
Before you get to that, what does it mean for the points to be symmetric about y = mx + b?

-Dan
 
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).

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?
 
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?

Thank you. I have been away from this site for more than 2 weeks.
 

Thread 'What Exactly is Dirac’s Delta Function? - Insight'

Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
View full post »

Thread 'Fermat's Last Theorem'

Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
View full post »
Thread 'Imaginary Pythagorus'

Thread 'Imaginary Pythagorus'

I posted this in the Lame Math thread, but it's got me thinking. Is there any validity to this? Or is it really just a mathematical trick? Naively, I see that i2 + plus 12 does equal zero2. But does this have a meaning? I know one can treat the imaginary number line as just another axis like the reals, but does that mean this does represent a triangle in the complex plane with a hypotenuse of length zero? Ibix offered a rendering of the diagram using what I assume is matrix* notation...
View full post »

Similar threads

MHB Finding the Equation of a Line Given Two Points
Replies
2
Views
1K
B A symmetric problem has an asymmetric solution - why?
Replies
21
Views
2K
MHB What is the equation of a line passing through (6, -3) with a y-intercept of 8?
Replies
4
Views
1K
I Finding the Largest (or smallest) Value of a Function - given some constant symmetric errors
Replies
3
Views
1K
MHB Find the equation of the line through (-9, 2); perpendicular to y= -1
Replies
6
Views
2K
MHB Max Value of $b$ for Real Roots of $f(x)$ and $g(x)$
Replies
2
Views
1K
MHB What Is the Equation of a Line Parallel to 4x + 5y = 20 Passing Through (0,0)?
Replies
28
Views
4K
MHB Find an equation of the line that is perpendicular to x - y + 2 = 0
Replies
5
Views
2K
MHB The Minimum Value of a Quadratic Function: A Question of Symmetry
Replies
3
Views
1K
MHB Point (a, b) Reflected About Two Lines
Replies
3
Views
2K

Hot Threads

Recent Insights

Back
Top