Find the x coordinate if the distance from point A (-6; x) to point C (6; 6) is 13.

In order to find the distance between points A (x1; y1) and B (x2; y2), you must use the formula:

S = ((x2 – x1) ^ 2 + (y2 – y1) ^ 2) ^ (1/2).

Since the distance between our points is known according to the conditions of the problem, the coordinates are also practically all known, we substitute the data into our formula:

13 = ((6 – (-6)) ^ 2 + (6-x) ^ 2) ^ (1/2). we put both sides of the equality in the square.

169 = 12 * 12 + (6-x) ^ 2.

25 = 36 – 12 * x + x ^ 2.

x ^ 2 – 12 * x + 11 = 0.

D = (144 – 44) ^ (1/2).

x1 = (80 ^ (1/2) + 12) / 2;

x2 = (12 – 80 ^ (1/2)) / 2.