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Plato Rozhkov
Plato Rozhkov

Midpoint High Quality


Likert-type scales are often used in survey instruments, and practitioners and researchers need to clearly understand the appropriate use of a midpoint in these scales. The authors of this article explore research studies from various disciplines to indicate that there are circumstances when a midpoint should be included and others where it should not. They provide tables, summarizing the benefits and problems in each case as well as evidence-based strategies to employ.




midpoint


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Midpoint refers to a point that is in the middle of the line joining two points. The two reference points are the endpoints of a line, and the midpoint is lying in between the two points. The midpoint divides the line joining these two points into two equal halves. Further, if a line is drawn to bisect the line joining these two points, the line passes through the midpoint.


The midpoint formula is used to find the midpoint between two points whose coordinates are known to us. The midpoint formula is also used to find the coordinates of the endpoint if we know the coordinates of the other endpoint and the midpoint. In the coordinate plane, if a line is drawn to connect two points (4, 2), and (8, 6), then the coordinates of the midpoint of the line joining these two points are (4 + 8/2, 2 + 6/2) = (12/2, 8/2) = (6, 4). Let us learn more about the formula of the midpoint, and different methods to find the midpoint of a line.


A midpoint is a point lying between two points and is in the middle of the line joining the two points. If a line is drawn joining the two points, then the midpoint is a point at the middle of the line and is equidistant from the two points. Given any two points, say A and C, the midpoint is a point B which is located halfway between points A and C. Therefore, to calculate the midpoint, we can simply measure the length of the line segment and divide by 2.


Observe that point B is equidistant from A and C. A midpoint exists only for a line segment. A line or a ray cannot have a midpoint because a line is indefinite in both directions and a ray has only one end and thus can be extended.


The midpoint formula is defined for the points in the coordinate axes. Let (x)1, (y)1 and (x)2, (y)2 be the endpoints of a line segment. The midpoint is equal to half of the sum of the x-coordinates of the two points, and half of the sum of the y-coordinates of the two points. The midpoint formula to calculate the midpoint of a line segment joining these points can be given as,


Let us look at this example and find the midpoint of two points in one-dimensional axis. Suppose, we have two points, 5 and 9, on a number line. The midpoint will be calculated as: (5 + 9)/2 = 14/2 = 7. So, 7 is the midpoint of 5 and 9.


Let's consider a line segment with its endpoints, (x)1, (y)1 and (x)2, (y)2. For any line segment, the midpoint is halfway between its two endpoints. The expression for the x-coordinate of the midpoint is [(x)1 + (x)2]/2, which is the average of the x-coordinates. Similarly, the expression for the y-coordinate is [(y)1 + (y)2]/2, which is the average of the y-coordinates.


Method 1: If the line segment is vertical or horizontal, then dividing the length by 2 and counting that value from any of the endpoints will get us the midpoint of the line segment. Look at the figure shown below. The coordinates of points A and B are (-3, 2) and (1, 2) respectively. The length of horizontal line \(\overlineAB\) is 4 units. Half of this length is 2 units. Moving 2 units from the point (-3, 2) will give (-1, 2). So, (-1, 2) is the midpoint of \(\overlineAB\).


Method 3: One way to find the midpoint of a line given in a plane is using construction. We can use a compass and straightedge construction to first construct a lens using circular arcs of equal (and large enough) radii centered at the two endpoints, then connecting the cusps of the lens (the two points where the arcs intersect). The point of intersection of the line connecting the cusps and the segment is the midpoint of the segment.


Example: Midpoint R between the points P and Q has the coordinates (4, 6). If the coordinates of Q are (8, 10), then what are the coordinates for point P? Solve it by using the midpoint formula.


The midpoint formula includes computations separately for the x-coordinate of the points, and the y-coordinate of the points. Further, the computations of points between two given points also include similar computation of the x-coordinate and the y-coordinate of the given points. The following two formulas are closely related to the midpoint formula.


The point of intersection of the medians of a triangle is called the centroid of the triangle. The median is a line joining the vertex to the midpoint of the opposite side of the triangle. The centroid divides the median of the triangle in the ratio 2:1. For a triangle with vertices (x)1, (y)1, (x)2, (y)2, (x)3, (y)3 the formula to find the coordinates of the centroid of the triangle is as follows.


The midpoint formula in coordinate geometry is defined as the formula to find the center point of a straight line, using the coordinates of its endpoints. The midpoint formula is used to find the halfway that is a point that divides the line into two equal parts.


For the midpoint of the line joining two points, whose coordinates are given, the midpoint formula in words can be described as half of the sum of the x-coordinates of the two points and half of the sum of the y-coordinates of the two points.


Yes, the midpoint value can also be a fraction. It is basically dependent on the numeric value of the two points. The midpoint is the sum of the numeric value of two points, divided by 2. For points such as -4 and 5 on the number line, the midpoint is +1/2.


The midpoint can be zero. This is dependent on the value of the two points. For two points on a number line on points with values -4, and 4, the midpoint is 0. And for two points such as (-2, 5), and (2, -5), the midpoint is equal to (0, 0).


The midpoint of a line is a point that is equidistant from the endpoints of the line and in the middle of the line. If the endpoints of the line are (x)1, (y)1, and (x)2, (y)2, then the formula for the midpoint of the line is [(x)1 + (x)2]/2, [(y)1 + (y)2]/2


The midpoint of the triangle is the centroid of the triangle. The centroid is the point of intersection of medians of a triangle. The center of gravity of any triangular-shaped object is at its centroid.


The midpoint of a circle is the center of the circle. The largest chord of the circle is the diameter, and the midpoint of the diameter of the circle is the midpoint of the circle. The midpoint of the circle is equidistant from every point on the circle.


Midpoint Discretionary Order (MDO) is a patent-pending feature having a blended order type that incorporates the characteristics of Primary Peg, Midpoint Peg and Discretionary orders. Members can use MDOs to post displayed or non-displayed liquidity at the National Best Bid/National Best Offer for Buy/Sell orders with a discretionary range extending to and including the NBBO midpoint. MDOs do not execute at a price more aggressive than the NBBO midpoint. MDO is available on EDGA and EDGX exchanges, providing the opportunity to use MDOs in two different trading markets that offer comparable MDO advantages, but also provide a few distinguishing characteristics to meet varying needs of investors.


In addition to QDP, Cboe will now allow MDO orders to include offset instructions. This will allow MDOs to be ranked at prices less or more aggressive than the NBB for buy orders or the NBO for sell orders, while still maintaining discretion to the NBBO midpoint, consistent with their limit price.


Order 2, which is an MDO to buy, is ranked at $9.99 non-displayed with discretion to the midpoint price of $10.005. When Order 3 is entered it will trade a single share with Order 1 at $10.00, triggering a QDP Active Period for Order 2 because of the execution of the EDGX Best Bid below one round lot. This restricts the ability for Order 2 to exercise discretion for two milliseconds, and prevents the execution of Order 4 within Order 2's discretionary range. As a result, the Order 4 would be cancelled without an execution.


In case of VRLA (gel or AGM) batteries, gassing due to overcharging will dry out the electrolyte, increasing internal resistance and ultimately resulting in irreversible damage. Flat plate VRLA batteries start to lose water when the charge voltage approaches 15V (12V battery). Including a safety margin, the midpoint deviation should therefore remain below 2% during charging. When, for example, charging a 24V battery bank at 28.8V absorption voltage, a midpoint deviation of 2% would result in:


Obviously, a midpoint deviation of more than 2% will result in overcharging the top battery and undercharging the bottom battery. These are two good reasons to set the midpoint alarm level at not more than d = 2%.


In case of a 48V battery bank consisting of 12V series connected batteries, the % influence of one battery on the midpoint is reduced by half. The midpoint alarm level can therefore be set at a lower level.


In case of series/parallel connection disconnect the midpoint, parallel connection wiring and measure the individual midpoint voltages during absorption charging to isolate batteries or cells which need additional charging.


The individual batteries or cells of a battery bank are not identical, and when fully discharging a battery bank, the voltage of some cells will start dropping earlier than others. The midpoint alarm will therefore nearly always trip at the end of a deep discharge.


If the midpoint alarm trips much earlier (and does not trip during charging), some batteries or cells may have lost capacity or may have developed a higher internal resistance than others. The battery bank may have reached the end of service life, or one or more cells or batteries have developed a fault: 041b061a72


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