Problema Solution
find the point with coordinates of the form (2a,a)that is in the third quadrant and is a distance 5 from P(1,3)
I know the answer is (-2,-1) but I have no idea how to get to that answer.
Answer provided by our tutors
Make a drawing and use the formula for distance between the 2 points (2a, a) and P(1,3)
(1 - 2a)^2 + (a - 3)^2 = 5^2
by solving the quadratic equation we find 2 roots
a = - 1 and a = 3
click here to see the step by step solution of the quadratic equation
since the point (2a, a) is in the third quadrant then a < 0 thus the solution is a = -1
(2a , a) = (2(-1), - 1) = (-2, -1)
the point has the coordinates (-2, -1).