Question

To minimize the sum of distances AB+BC, what is the value of x in the points a=(−1,5), b=(x,2), and c=(4,−6)?

a) 0
b) 2
c) 3
d) 5

Answer 1

To minimize the sum of distances AB+BC, we need to find the value of x that will make the distance AB as short as possible.

Step-by-step explanation:

To minimize the sum of distances AB+BC, we need to find the value of x that will make the distance AB as short as possible. The formula for the distance between two points (x1, y1) and (x2, y2) is given as sqrt((x2-x1)^2 + (y2-y1)^2). In this case, the distance AB can be written as sqrt((x+1)^2 + (2-5)^2). To minimize this distance, we need to find the value of x that will make this expression as small as possible. To do this, we can take the derivative of the expression with respect to x and set it equal to 0. Solving this equation will give us the value of x that minimizes the distance AB.