Question

Point b has coordinates ​(1​,2​). the​ x-coordinate of point a is negative −11. the distance between point a and point b is 15 units. what are the possible coordinates of point​ a?

Answer 1

The distance between points is given by the following equation:
d = root ((x2-x1) ^ 2 + (y2-y1) ^ 2)
Substituting we have:
15 = root ((- 11-1) ^ 2 + (a-2) ^ 2)
We clear the value of a:
(15) ^ 2 = (root ((- 11-1) ^ 2 + (a-2) ^ 2)) ^ 2
225 = (- 11-1) ^ 2 + (a-2) ^ 2)
Rewriting:
225 = 144 + (a-2) ^ 2
225-144 = (a-2) ^ 2
81 = (a-2) ^ 2
a-2 = +/- root (81)
a = +/- 9 + 2
The possible values are:
a1 = 9 + 2 = 11
a2 = -9 + 2 = -7
Then, the possible coordinates of point a are:
(-11, 11)
(-11, -7)
Answer:
the possible coordinates of point a are:
(-11, 11)
(-11, -7)