Question

An equilateral triangle on the coordinate plane has vertices at (–1, 2) and (4, 2). What are the possible coordinates of the third vertex rounded to the nearest tenth?

Answer 1

(1.5 , 6.33) or (1.5 , - 2.33)

Explanation:

Answer 2

(1.5 , 6.33) or (1.5 , - 2.33)

Explanation:

The vertex will something at the line perpendicular to Two end points of the base and intercept the midpoint of two end points, it can be either upward or downward.

mid point: ((-1 + 4) / 2 , (2 + 2) / 2), i.e. (1.5 , 2)

Base length: 4 - (-1) = 5

Vertex coordinate ( 1.5 , y)

length between (4 , 2) and (1.5 , y) is 5

(4 - 1.5)² + (2 - y)² = 5²

6.25 + (2 - y)² = 25

(2 - y)² = 18.75

2 - y = ± 4.33

y = 6.33 or - 2.33