Given points A (2; 5; 8) and B (6; 1; 0), find a) on the ordinate point C, equidistant from points A and B.

Point C lies on the ordinate, which means that its two coordinates, x and z, are equal to zero. C (0; y; 0). It remains to find its coordinate y. Knowing that point C is equidistant from points A and B, we can write down the distances AC and BC, and equate them. We get an equation, solving which we find the coordinate at point C.

AC ^ 2 = (0-2) ^ 2 + (y-5) ^ 2 + (0-8) ^ 2 = 4 + y ^ 2 -10y +25 + 64 = y ^ 2 – 10y +93

BC ^ 2 = (0-6) ^ 2 + (y-1) ^ 2 + (0-0) ^ 2 = 36 + y ^ 2 -2y + 1 = y ^ 2 – 2y +37

y ^ 2 – 10y +93 = y ^ 2 – 2y +37

y ^ 2 – y ^ 2 -10y + 2y = 37 – 93

-8y = -56

y = 7. Point C has coordinates (0; 7; 0)