You are positioning an isosceles triangle to do a coordinate proof. You decide to place the base of the triangle on the x-axis, with one of the base angles at the origin, the other base angle at (2g, 0), and the vertex angle at (g, h).
Give the coordinates of the following locations, and the area of the triangle.
Location | Coordinates
The midpoint of the base | (g,0)
The midpoint of the left side | (g/2,h/2)
The midpoint of the right side | __________
Area of the triangle: GH
What is the midpoint of the right side?
Give the coordinates of the following locations, and the area of the triangle.
Location | Coordinates
The midpoint of the base | (g,0)
The midpoint of the left side | (g/2,h/2)
The midpoint of the right side | __________
Area of the triangle: GH
What is the midpoint of the right side?
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Since the triangle is symmetric about the vertical line x = g, the midpoint of the right side is the reflection of the midpoint of the left side about x = g, (3g/2, h/2)
Or:
Midpoint of the right side is halfway between the midpoint of the base and the right end of the base and at 1/2 the height of the triangle, (3g/2, h/2)
Or:
Midpoint of the right side is halfway between the midpoint of the base and the right end of the base and at 1/2 the height of the triangle, (3g/2, h/2)