Question

If P=(-2,5) and (x,-27), find all numbers x such that the vector represented by PQ has length -40

Answer 1

x ∈ {-26, 22}

Explanation:

A graph shows that the points (-26, -27) and (22, -27) lie on a circle of radius 40 centered at (-2, 5). That is, if Q is either one of these points, the vector PQ will have a length of 40:

• √((-26-(-2))^2 +(-27-5)^2) = √((-24)^2 +(-32)^2) = √1600 = 40
• √((22 -(-2))^2 +(-27 -5)^2) = √(24^2 +(-32)^2) = √1600 = 40

You can call it -40 if you like, but you have to define what negative length means when you do that.