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


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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).