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How do you form an equation for the perpendicular bisector of the line segment joining the points of p q and 7p 3q showing all details of your work?
First find the midpoint the slope and the perpendicular slope of the points of (p, q) and (7p, 3q)
Midpoint = (7p+p)/2 and (3q+q)/2 = (4p, 2q)
Slope = (3q-q)/(7p-p) = 2q/6p = q/3p
Slope of the perpendicular is the negative reciprocal of q/3p which is -3p/q
From the above information form an equation for the perpendicular bisector using the straight line formula of y-y1 = m(x-x1)
y-2q = -3p/q(x-4p)
y-2q = -3px/q+12p2/q
y = -3px/q+12p2/q+2q
Multiply all terms by q and the perpendicular bisector equation can then be expressed in the form of:-
3px+qy-12p2-2q2 = 0
What else can I help you with?
What is the difference between a perpendicular line and a perpendicular bisector?
A perpendicular line is one that is at right angle to another - usually to a horizontal line. A perpendicular bisector is a line which is perpendicular to the line segment joining two identified points and which divides that segment in two.
Determine an equation for the right bisector of the line segment joining A 3and6 and B-1and2?
x2-x1,y2-y1
What is the perpendicular bisector equation of the line joined by the points 11 13 and 17 19 showing work and answer?
The equation of a line through point (x0, y0) with gradient m is given by:y - y0 = m(x - x0)The gradient (m) of a line between two points (x0, y0) and (x1, y1) is given by:m = change_in_y/change_in_x = (y1 - y0)/(x1 - x0)→ The equation of the line between (11, 13) and (17, 19) is given by:y - 13 = (19-13)/(17-11) (x - 11)→ y - 13 = 6/6 (x - 11)→ y - 13 = x - 11→ y = x + 2and its gradient is m = 1.The gradient (m') of a line perpendicular to a line with gradient m is such that mm' = -1, ie m' = -1/m→ The gradient of the perpendicular line to the line between (11, 13) and (17, 19) has gradient m' = -1/1 = -1.The perpendicular bisector goes through the point midway between (11, 13) and (17, 19) which is given by the average of the x and y coordinates: ((11+17)/2, (13+19)/2) = (14, 16)Thus the perpendicular bisector of the line joining (11, 13) to (17,19) is given by:y - 16 = -1(x - 14)→ y - 16 = -x + 14→ y + x = 30Which in its general form is: x+y-30 = 0
What are the values of b and c when y plus 4x equals 11 is the perpendicular bisector line of the line joining b 2 to 6 c on the Cartesian plane?
If the points are (b, 2) and (6, c) then to satisfy the straight line equations it works out that b = -2 and c = 4 which means that the points are (-2, 2) and (6, 4)
What letters in the English language have both parallel and perpendicular lines?
There are letters in the alphabet with both parallel and perpendicular lines. In alphabetical order, they are E, F, and H. If the joining point can be considered perpendicular and parallel, then B, D, P, and R also match the criterion.
What is a characteristic of a perpendicular bisector?
Given a straight line joining the points A and B, the perpendicular bisector is a straight line that passes through the mid-point of AB and is perpendicular to AB.
What is the perpendicular bisector equation joining the line segment of -2 plus 5 and -8 -3 giving brief details?
Points: (-2, 5) and (-8, -3) Midpoint: (-5, 1) Slope: 4/3 Perpendicular slope: -3/4 Use: y-1 = -3/4(x--5) Bisector equation: y = -3/4x-11/4 or as 3x+4y+11 = 0
How do you find the midpoint the slope the perpendicular slope and the equation for the perpendicular bisector of the line segment joining the points of 3 5 and 7 7?
Midpoint = (3+7)/2, (5+7)/2 = (5, 6) Slope of line segment = 7-5 divided by 7-3 = 2/4 = 1/2 Slope of the perpendicular = -2 Equation of the perpendicular bisector: y-y1 = m(x-x1) y-6 =-2(x-5) y = -2x+10+6 Equation of the perpendicular bisector is: y = -2x+16
What is the difference between a perpendicular line and a perpendicular bisector?
A perpendicular line is one that is at right angle to another - usually to a horizontal line. A perpendicular bisector is a line which is perpendicular to the line segment joining two identified points and which divides that segment in two.
What is the equation for the perpendicular bisector of the line segment joining the points of 3 5 and 7 7?
y = -2x+16 which can be expressed in the form of 2x+y-16 = 0
What are the values of a and b given that y plus 4x equals 11 is the perpendicular bisector equation of the line joining a 2 to 6 b?
Their values work out as: a = -2 and b = 4
What is the locus of points equidistant from two points?
The perpendicular bisector of the straight line joining the two points.
What describes the Locus of all points that are equidistant from 2 lines?
The perpendicular bisector of the line joining the two points.
What is the perpendicular bisector equation joining the points of s 2s and 3s 8s on the Cartesian plane showing work?
Points: (s, 2s) and (3s, 8s) Slope: (8s-2s)/(3s-s) = 6s/2s = 3 Perpendicular slope: -1/3 Midpoint: (s+3s)/2 and (2s+8s)/2 = (2s, 5s) Equation: y-5s = -1/3(x-2s) => 3y-15s = -1(x-2s) => 3y = -x+17x Perpendicular bisector equation in its general form: x+3y-17s = 0
What is the locus of points equidistant from two points A and B that are 8 meters apart?
It is the perpendicular bisector of AB, the line joining the two points.
What is the equation and its perpendicular bisector equation of the line joining the points of 1 2 and 3 4 showing work?
1 Points: (1, 2) and (3, 4) 2 Slope: (2-4)/(1-3) = 1 3 Perpendicular slope: -1 4 Midpoint: (1+3)/2 and (2+4)/2 = (2, 3) 5 Equation: y-2 = 1(x-1) => y = x+1 6 Bisector equation: y-3 = -1(x-2) => y = -x+5
Determine an equation for the right bisector of the line segment joining A 3and6 and B-1and2?
x2-x1,y2-y1
