Question

Find the possible values of A if the points with the given coordinates are the indicated distance apart: (6, 2) and (-2, A) with a distance of √185. What are the potential values of A to satisfy this condition?

Answer 1

The potential values of A that make the distance between points (6, 2) and (-2, A) √185 are 13 and -9.

Step-by-step explanation:

To find the potential values of A for which the distance between points (6, 2) and (-2, A) is √185, we can use the distance formula derived from the Pythagorean theorem. This formula calculates the distance (d) between two points (x1, y1) and (x2, y2) in a Cartesian plane as:

d = √((x2 - x1)2 + (y2 - y1)2)

Plugging our values into this formula:

√185 = √((-2 - 6)2 + (A - 2)2)

Simplifying further we get:

185 = 64 + (A - 2)2

(A - 2)2 = 121

A - 2 = ±11

Therefore, there are two potential values for A:

• 
  
• A = 2 + 11 = 13
• 
  
• A = 2 - 11 = -9

Both A = 13 and A = -9 satisfy the condition that the distance between the two points is √185.