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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
Which type of triangle will always have a perpendicular bisector that is also an angle bisector?
An isosceles triangle will always have a perpendicular bisector that is also an angle bisector. In an isosceles triangle, the two sides are of equal length, and the perpendicular bisector of the base (the unequal side) also divides the vertex angle into two equal angles, thus serving as an angle bisector as well.
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 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
Which type of triangle will always have a perpendicular bisector that is also an angle bisector?
An isosceles triangle will always have a perpendicular bisector that is also an angle bisector. In an isosceles triangle, the two sides are of equal length, and the perpendicular bisector of the base (the unequal side) also divides the vertex angle into two equal angles, thus serving as an angle bisector as well.
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.
How many bisectors could a segment have?
A segment has exactly one bisector. This bisector is a line (or line segment) that divides the original segment into two equal parts and is perpendicular to it. No matter the length of the segment, the unique bisector will always pass through the midpoint of the segment.
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
