Question

Francesca is writing a coordinate proof to show that the diagonals of a rectangle divide the rectangle into four triangles of equal area

Are my fill in’s right!? Please help ••!!!!

Answer 1

Answers are

1) 2x

2) y

3) xy

4) 2x

5) x

Took the test

Explanation:

Answer 2

Step-by-step explanation:

Since PQRS is a rectangle ,

The x- coordinate for S and R is same . The x coordinate of S is 2x

So R is (2x, 2y)

Mid point of 2x is x and mid point of 2y is y

Diagonals of a rectangle bisect each other so coordinate of T are (x,y)

In triangle PTQ, the length of the base is 2y and height is x

We know area of triangle is
`(1)/(2)* base * height`

`(1)/(2)* 2y * x`= xy

Area of the triangle PTQ is xy

In triangle RTQ, the length of the base is 2x and height is y

area of triangle is
`(1)/(2)* base * height`

`(1)/(2)* 2x * y`= xy

In triangle RTS, the length of the base is 2y and height is x

We know area of triangle is
`(1)/(2)* base * height`

`(1)/(2)* 2y * x`= xy