Answer:

To find the point A (a,6) that is equidistant from points B (2, 8) and C (1,1), we can use the distance formula. The distance between two points (x1,y1) and (x2,y2) is given by:

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

Since A is equidistant from B and C, we have:

d(A,B) = d(A,C)

Using the distance formula, we can write:

sqrt((a - 2)^2 + (6 - 8)^2) = sqrt((a - 1)^2 + (6 - 1)^2)

Simplifying this equation gives:

(a - 2)^2 + 4 = (a - 1)^2 + 25

Expanding the squares and simplifying further gives:

a^2 - 4a + 20 = a^2 - 2a + 26

Solving for a gives:

a = -3

Therefore, the point A that is equidistant from points B and C is (-3,6)1.

I hope this helps! Let me know if you have any other questions.