In the xy-plane, an equilateral triangle has vertices at (0, 0) and (9

If you look at all the answers choices, they all appear in quadrant 1.

Since the one side lies down along the X Axis and is 9 units (from (0 , 0) to (9 , 0))

the Height of the equilateral triangle will extend vertically from the X Axis into Quadrant 1

Rule: from any vertex, the Height = perpendicular Bisector = median = angle Bisector

Rule: the Height for a particular given equilateral triangle is given by——->

Height = (side) * sqrt(3) * (1/2)


Since the Height will also be the Median and perpendicular Bisector of the 9 unit side along the X Axis, the X coordinate of the 3rd unknown Vertex should be at the midpoint of the 2 Given vertices’ X Coordinates:

(9 + 0) / 2 = 4.5 = X Coordinate


Furthermore, from this X coordinate, we can find vertex’s accompanying Y Coordinate by finding the Height of an equilateral triangle of Side length 9 and extending that Height’s length up on Y Axis

Height = (9) * sqrt(3) * (1/2) = Y Coordinate


Thus, the coordinates of the 3rd vertex will be:

(4.5 ; 9 * sqrt(3) * (1/2) )

E

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