We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.

An equilateral triangle has two vertices at (0,5) and (8,5). If the third vertex is in the first quadrant, what is the y-coordinate? Express your answer in simplest radical form.


 Feb 17, 2019

\(\text{The point will have it's }x \text{ coordinate at the midpoint of the given points}\\ x=4\\ \text{the distance from the point to say }(0,5) \text{ is equal to the (squared) distance between the given points}\\ (4-0)^2+(y-5)^2 = 8^2\\ 16 + (y-5)^2 = 64\\ (y-5)^2 = 48\\ y = \pm \sqrt{48}+5 = \pm 4\sqrt{3}+5\\ \text{the point that lies in the first quadrant is thus }\\ (x,y) = (4, 4\sqrt{3}+5)\)

 Feb 17, 2019

11 Online Users