A segment bisector is an object that passes through the midpoint of a segment, bisecting it or dividing it into two segments of equal length. The object can be a line segment, line, ray, or a plane that passes though the midpoint.
Identify the segment bisector and find the length of the segment
Identify the segment bisector of Then find the length of
ConstructionBisect a Segment
To bisect a segment means to draw the object that bisects it, or passes through its midpoint. Here it will be shown how to draw the line that bisects
Place a compass with its pointy end at one of the segment's end-points. Draw a large arc that intersects the segment further away than the midpoint.
Keep the compass set on the same length and place its pointy end at the other end of the segment. Draw another large arc across the segment.
If the arcs have been drawn large enough, they will now intersect each other twice. If they don't, extend them. Next use a ruler to draw a line through the two points where the arcs intersect each other.
The last step is to erase the arcs and draw an arrow on each end of the line.
The midpoint, between two points, and can be determined using the midpoint formula. The coordinates for the midpoint can be seen as half of the horizontal and vertical distance.
Consider shown in the coordinate plane below. The horizontal and vertical distance, and respectively, between its endpoints are shown.
The midpoint of this segment, divides the distance between its endpoints exactly in half both horizontally and vertically. That means, the distance from each endpoint to the midpoint is half of the established distances.
Find the midpoint of the segment
The segment has the endpoints and Find its midpoint,
Sometimes, it is necessary to divide a segment into two pieces that are not of equal length. This can be done when the endpoints of the segment and the desired ratio of the lengths are known. For example, find the point that divides so that the ratio of to is
Since the desired ratio is consider dividing into total pieces — spans of those pieces, and spans Choosing point as a starting point, will lie of the way to
- If the entire horizontal distance is gives the horizontal distance from to — units.
- If the entire vertical distance is gives the vertical distance from to — units.
Find the distance between the points
Find the distance between the points and
To find the perimeter of a shape in the coordinate plane, it is necessary to see each side of the shape as a line segment. When the coordinates of the vertices are known, the length of each side can be calculated separately using the distance formula.
The length of the perimeter is then found by adding the lengths of the sides.
Area is usually calculated using different formulas. However, for some shapes, one formula is not enough. Consider the example shown below.
Find the area and the perimeter
Find the area and the perimeter of the rectangle.
To begin, before we can calculate the area and perimeter of the rectangle, we need to know the lengths of the sides. Since the quadrilateral is a rectangle, the top and bottom have equal lengths and the sides have equal lengths. We'll find the length of the right side, and the length of the bottom. Since the coordiantes are given, we can use the distance formula. We'll determine first.
Now that the dimensions of the rectangle are known, the area, can be found by multiplying the length and the width, and the perimeter, can be found by adding all four sides. Thus, the area is square units and the perimeter is approximately units.