Answer:
two vertex are: (1 , 6.2) , (1 , - 4.2)
Step-by-step 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)
The two possible coordinates of the vertex are: (1, 6.2) , (1 , - 4.2)
A coordinate plane is a 2D plane which is formed by the intersection of two perpendicular lines known as the x-axis and y-axis.
A(-2, 1) and B (4, 1) AB is a parallel segments 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)
Therefore the two possible coordinates of the vertex are: (1, 6.2) , (1 , - 4.2)
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