Question

Prove: The segments joining the midpoints of the opposite sides of a quadrilateral bisect each other.

Answer 1

Quadrilateral ABCD as EFGH, going dextrorotary from the higher left.

 

E (x1, y1)

F (x2, y2)

G (x3, y3)

H (x4, y4)

 

midpoint of EF is (X1 + x2) / 2, (y1 + y2) / 2

midpoint of GH is (x3 + x4) / 2, (y3 + y4) / 2

midpoint of EH is (x1 + x3) / 2. (y1 + y3) / 2

midpoint of FG is (x2 + x3) / 2, (y2 + y3) / 2

 

The midpoints of each bisector square measure so (x1 + x2 + x3 + x4) / 2, (y1 + y2 + y3 + y4) / 2

 

end of proof

Further explanation

The midpoint is the center of the circle which, if measured by the fingers, is always the same (the finger). The midpoint or center point is the point that is in the middle of the circle.

The midpoint of the line segment is the point that is located right in the middle of the two endpoints. Thus, the midpoint is the average of the two endpoints, which is the average of two x coordinates and two y coordinates.

The midpoint formula can be used by adding the x coordinates of two endpoints and dividing the results by two, and then adding the y coordinates of the endpoints and dividing by two. This is how you find the average x and y coordinates of the endpoints. Here's the formula: [(x1 + x2) / 2, (y1 + y2) / 2]

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Calculate the Midpoint brainly.com/question/9404333

the formula brainly.com/question/11740317

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class: high school

subject: mathematics

keywords: midpoint, formula, coordinates

Answer 2

Answer:

$R=(\dfrac{b}{2},0)$

$S=(\dfrac{b+c}{2},\dfrac{d}{2})$

$T=(\dfrac{c+e}{2},\dfrac{d+f}{2})$

$U=(\dfrac{e}{2},\dfrac{f}{2})$

$M=(\dfrac{b+c+e}{4},\dfrac{d+f}{4})$

$M=(\dfrac{c+b+e}{4},\dfrac{d+f}{4})$

Step-by-step explanation:

We are given coordinates as:

$A(0,0)\ ,\ B=(b,0)\ ,\ C=(c,d)\ ,\ D=(e,f)\\\\R=(\dfrac{b}{2},0)\ ,\ S=(\dfrac{b+c}{2},\dfrac{d}{2})\ ,\ U=(\dfrac{e}{2},\dfrac{f}{2})\ ,\ T=(\dfrac{c+e}{2},\dfrac{d+f}{2})$

Now, it is given that M is the mid-point of the line segment RT and of US.

Hence, the coordinates of M is given as:

By taking the mid-point of side RT.

$M=(\dfrac{\dfrac{b}{2}+\dfrac{c+e}{2}}{2},\dfrac{0+\dfrac{d+f}{2}}{2}})\\\\\\i.e.\\\\\\M=(\dfrac{b+c+e}{4},\dfrac{d+f}{4})$

By taking the mid-point of side US.

$M=(\dfrac{\dfrac{e}{2}+\dfrac{b+c}{2}}{2},\dfrac{\dfrac{f}{2}+\dfrac{d}{2}}{2})\\\\\\i.e.\\\\\\M=(\dfrac{b+c+e}{4},\dfrac{d+f}{4})$