Question

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

Midpoints of both segments are the same point; therefore, segments bisect each other.

(fill in the blanks of the equation in the second picture with the correct number/letter/sign based off the first picture.)

Answer 1

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.

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

Answer 2

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]

learn more

Calculate the Midpoint https://brainly.com/question/9404333

the formula https://brainly.com/question/11740317

details

class: high school

subject: mathematics

keywords: midpoint, formula, coordinates