Question

Vanessa draws one side of an equilateral triangle ABC on the coordinate plane at points A(-2, 1) and B (4, 1). What are the two possible coordinates of vertex C? Round to the nearest tenth.

Answer 1

two vertex are: (1 , 6.2) , (1 , - 4.2)

Explanation:

A(-2, 1) and B (4, 1) AB is a parallel segment with x axis

The 3rd vertex P (x , y) will locate at the mid point of AB

x = (-2) + (4 - (-2)) /2 = 1 P (1 , y)

length AB = 4 - (-2) = 6

AP = AB (equilateral)

BP² = (4 - 1)² + (1 - y)² = 6²

1 - 2y + y² = 36 - 9 = 27

y² - 2y -26 = 0

y = ((-(-2)) ± √(-2)² - 4 x (-26)) / 2 = (2 ± √108) / 2 = 1 ± 5.2

y = 6.2 or y = -4.2

P (1 , 6.2) or P ( 1 , -4.2)