Posted by **Ruth** on Sunday, September 29, 2013 at 1:59am.

Consider two points A=(2,5) and B=(4,3), and a third point P=(a,b) on the x-axis. If the minimum value of line PA^2+ line PB^2 is c, what is a+b+c?

- Algebra -
**Steve**, Sunday, September 29, 2013 at 6:20am
well, b=0 (duh), so

PA^2 = (a-2)^2 + 5^2

PB^2 = (a-4)^2 + 3^2

so you want the minimum value of

(a-2)^2 + 5^2 + (a-4)^2 + 3^2 = 2a^2 - 12a + 54

you know the vertex is at (3,36).

## Answer this Question

## Related Questions

- algebra - In a coordinate plane, the points (2,4) and (3,-1) are on a line. ...
- Math - There are two points A=(2,0) and B=(4,0) and a moving point P=(t,t) on ...
- Algebra - Which of the following represent the equation of the line passing ...
- geometry - Joey plots a point P on the line AB, as shown. Which statement is ...
- Algebra - Given a line containing the points(1,4), (2,7) and (3,10) determine ...
- calculus - Consider line segments which are tangent to a point on the right half...
- math (calculus) - A line segment has one endpoint, A, on the x-axis and the ...
- Calculus - Consider line segments which are tangent to a point on the right ...
- Maths - Consider the line passing through two points P=(1,8) and Q=(−1,3...
- Calc - A line tangent to y=(x^2)+1 at x=a, a>0, intersects the x-axis at ...