Question

For what values of a is the distance between P(a,3) and Q(2,-1) minimized?

A) a = 3
B) a = 1
C) a = 2
D) a = 0

Answer 1

To minimize the distance between points P(a,3) and Q(2,-1), we use the distance formula and find that the distance is minimized when a = 2.

Step-by-step explanation:

To find the minimum distance between points P(a,3) and Q(2,-1), we can use the distance formula. The distance formula is given by:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Substituting the given coordinates into the formula, we have:

d = sqrt((2 - a)^2 + (-1 - 3)^2)

To minimize the distance, we want to find the value of a that makes this expression as small as possible. Taking the derivative of this expression with respect to a and setting it to zero, we can solve for a.

By solving this equation, we find that the distance between points P(a,3) and Q(2,-1) is minimized when a = 2. Therefore, the correct answer is C) a = 2.