4.09 Quiz: Coordinate Proofs Amira is writing a coordinate proof to show that the area of a triangle created by joining the midpoints of an isosceles triangles is
one-fourth the area of the isosceles triangle. She starts by assigning coordinates as given
ERR20)
DIO, OD
A28,0) R4,0)
Enter your answers, in simplest form, in the boxes to complete the coordinate proof
Point Q is the midpoint of DE, so the coordinates of point Q are (a, b).
Point Ris the midpoint of FE so the coordinates of point Rare
b).
In A DEF the length of the base, DF, is
and the height is 2b, so its area is
In A QRP, the length of the base, QR is
| and the height is b, so its area is ab.
Comparing the expressions for the areas proves that the area of the triangle created by joining the
midpoints of an isosceles triangle is one-fourth the area of the triangle.
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2
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4
Finish