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What is the length of the line and its perpendicular bisector equation that spans the points of 2 3 and 5 7 showing key stages of work?
Wiki User
∙ 9y ago
Points: (2, 3) and (5, 7)
Length of line: 5
Slope: 4/3
Perpendicular slope: -3/4
Midpoint: (3.5, 5)
Bisector equation: 4y = -3x+30.5 or as 3x+4y-30.5 = 0
Wiki User
∙ 9y ago
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What is the length of the line and its equation including its perpendicular bisector equation that spans the points of 2 3 and 5 7 on the Cartesian plane showing key stages of work?
Points: (2, 3) and (5, 7)Length: 5 unitsSlope: 4/3Perpendicular slope: -3/4Midpoint: (3.5, 5)Equation: 3y = 4x+1Bisector equation: 4y = -3x+30.5
What are the distances from a point on the perpendicular bisector to the endpoints of a segment?
The distance will be length of the line divided by 2 because the perpendicular bisector cuts through the line at its centre and at right angles
How does midpoint and distance formula fit into the big picture of math?
The mid-point is needed when the perpendicular bisector equation of a straight line is required. The distance formula is used when the length of a line is required.
What is the length of the line and its perpendicular bisector equation whose equation is 4x plus 3y equals 24 that spans the x and y axes?
4x + 3y = 24 crosses the axes at (6, 0) and (0, 8). Therefore its length is [(6 - 0)2 + (0 - 8)2]1/2 = [36 + 64]1/2 = 1001/2 = 10 Mid point = (3, 4) Gradient of given line = -4/3 So gradient of perpendicular bisector = 3/4 Therefore equation of perp bisector: (y - 4) = 3/4(x - 3) or 4y - 16 = 3x - 9 3x - 4y = -7
What are each point on the bisector of an angle that is equidistant from the sides of the angle?
Every point on the bisector of an angle is equidistant from the sides of that angle. It is understood that the distance of a point from a line is the length of the perpendicular dropped from the point to the line.
What is the length of the line and its equation including its perpendicular bisector equation that spans the points of 2 3 and 5 7 on the Cartesian plane showing key stages of work?
Points: (2, 3) and (5, 7)Length: 5 unitsSlope: 4/3Perpendicular slope: -3/4Midpoint: (3.5, 5)Equation: 3y = 4x+1Bisector equation: 4y = -3x+30.5
What are the distances from a point on the perpendicular bisector to the endpoints of a segment?
The distance will be length of the line divided by 2 because the perpendicular bisector cuts through the line at its centre and at right angles
How does midpoint and distance formula fit into the big picture of math?
The mid-point is needed when the perpendicular bisector equation of a straight line is required. The distance formula is used when the length of a line is required.
When constructing a perpendicular bisector why must the compass opening be greater than the length of the segment?
So that the arc is mid-way in perpendicular to the line segment
Why can't a line or ray have a perpendicular bisector?
Because both lines and rays are infinite in length and thus have no midpoint.
What is the length of the line and its perpendicular bisector equation whose equation is 4x plus 3y equals 24 that spans the x and y axes?
4x + 3y = 24 crosses the axes at (6, 0) and (0, 8). Therefore its length is [(6 - 0)2 + (0 - 8)2]1/2 = [36 + 64]1/2 = 1001/2 = 10 Mid point = (3, 4) Gradient of given line = -4/3 So gradient of perpendicular bisector = 3/4 Therefore equation of perp bisector: (y - 4) = 3/4(x - 3) or 4y - 16 = 3x - 9 3x - 4y = -7
What are each point on the bisector of an angle that is equidistant from the sides of the angle?
Every point on the bisector of an angle is equidistant from the sides of that angle. It is understood that the distance of a point from a line is the length of the perpendicular dropped from the point to the line.
What is the perpendicular distance from the coordinates of 7 and 5 to the straight line of 3x plus 4y -16 equals 0 showing key stages of work?
Points: (7, 5) Equation: 3x+4y-16 = 0 Perpendicular equation: 4x-3y-13 = 0 Equations intersect at: (4, 1) Length of perpendicular line: 5
What is the length of the line including its equation and its perpendicular bisector equation that spans the points of 2 3 and 5 7 showing work?
Points: (2, 3) and (5, 7)Midpoint: (2+5)/2 and (3+7)/2 = (3.5, 5)Length: square root of (2-5)2+(3-7)2 = 5Slope: (3-7)/(2-5) = 4/3Perpendicular slope: -3/4Equation: y-3 = 4/3(x-2) => 3y = 4x+1Perpendicular equation: y-5 = -3/4(x-3.5) => 4y = -3x+30.5
What is the perpendicular line length from coodinates of 7 and 5 to the straight line equation 3x plus 4y -16 equals 0 showing work?
1 Point of origin: (7, 5) 2 Equation: 3x+4y-16 = 0 3 Perpendicular equation: 4x-3y-13 = 0 4 Both equations intersect at: (4, 1) 5 Line length is the square root of: (7-4)2+(5-1)2 = 5
Cana line segment lack a bisector?
No. A line of any length can be divided in half - and that is what a bisector is.
How do you draw a perpendicular bisector?
Drawing perpendicular bisector for a line:Place the sharp end of a pair of compasses at one end of the line, and open it to just over half of the line. Draw an arc which must intersect the line in the position described. Then put the sharp end at the other of the line and, keeping the compassing at the same length, draw another arc which intersects the first one twice and also the line. Then draw a straight line through the two places where the arcs intersect. This line is the perpendicular bisector. Drawing perpendicular bisector of angle:Places the sharp end of the compass at the point of the angle and, after having opened it arbitraily wide, draw an arc which intersects the two lines meeting to form the angle each once in the said position. Then remove the compass and, always keeping it opened at the SAME length, place the sharp end at each of the two places where the previous arc cuts each of the two lines meeting to form the angle. In this position with the described length, draw a small arc at each of the said places, which should cross each other. Draw a straight line from the point of the angle to this crossing. This should be the bisector of the angle.
