Answer:
Refer to the attached image.
Given: A quadrilateral ABCD, where P, Q, R and S are the mid points of the sides AD, AB, BC, CD respectively.
To prove: The segments joining the mid points of the opposite sides of a quadrilateral bisect each other that is OP=OR and OQ=OS.
Proof: Join the segment BD.
Consider the triangle ABD,
Since P is the mid point of AD and Q is the mid point of AB.
Therefore, [tex]PQ \parallel BD, PQ=\frac{1}{2} BD[/tex].... (Equation 1)
[Line segments joining the mid points of two sides of a triangle is parallel to the third side and is also half of it]
Consider the triangle BCD,
Since S is the mid point of CD and R is the mid point of BC.
Therefore, [tex]SR \parallel BD, SR=\frac{1}{2} BD[/tex].... (Equation 2)
[Line segments joining the mid points of two sides of a triangle is parallel to the third side and is also half of it]
By equations 1 and 2, we get
[tex]PQ=SR, PQ \parallel RS[/tex]
Therefore, PQRS is a parallelogram as opposite sides are equal and parallel.
In a parallelogram, diagonals bisect each other.
Since, PR and QS are the diagonals of the parallelogram PQRS.
Therefore, OP=OR and OQ=OS.
Hence, proved.
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
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 https://brainly.com/question/9404333
the formula https://brainly.com/question/11740317
details
class: high school
subject: mathematics
keywords: midpoint, formula, coordinates
