Question

Andrew is writing a coordinate proof to show that the triangle formed by connecting the midpoints of the sides of an isosceles triangle is itself an isosceles triangle. He starts by assigning coordinates as given.

Answer 1

Coordinates of P: (a,b)
coordinates of Q:(3a,b)
coordinates of R:(2a,0)

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Answer 2

Answer: Coordinate of P = (a,b)

Coordinate of Q = (3a,b)

Coordinates of r= (2a,0)

Step-by-step explanation:

Andrew draw mid points P,Q and R on the sides of triangle DEF at DE,DF and EF respectively.

To fill the boxes we need to find the coordinates of the midpoints

As P is the mid point of DE then  coordinate of P =$(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})=(\frac{2a+0}{2},\frac{2b+0}2{})=(a,b)$

Similarly Q is the midpoint of DF then coordinates of Q=$(\frac{2a+4a}{2},\frac{2b+0}2{})=(3a,b)$

Now, R is the midpoint of EF then coordinates of r =$=(\frac{4a+0}{2},\frac{0+0}2{})=(2a,0)$