Let P = (7, 3) and Q = (-6, 1)
Then mid point of PQ = ((7-6)/2, (3+1)/2) = (1/2, 2)
Also, gradient of PQ = (3 - 1)/(7 + 6) = 2/13
So the gradient of the perpendicular = -13/2
Therefore the required line passes through the point (1/2, 2) and has gradient -13/2
and so its equation is (y - 2) = -13/2*(x - 1/2)
or 4y - 8 = -26x + 13
that is 26x + 4y - 21 = 0
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.
The perpendicular bisector of the straight line joining the two points.
For triangle ABC, find the midpoint of side BC. Then, find the slope of side BC and use its negative reciprocal (since the negative reciprocal slope is the slope of the right bisector joining side BC and the opposite vertex). Finally, substitute the midpoint and negative reciprocal slope into the y=mx+b equation to get "b", then write the equation. :)
The slope of the line joining the two pints is (4 - 2)/(-3 - 0) = -2/3 Therefore the slope of the perpendicular is 3/2
answerDraw two lines of equal lengths perpendicular to AB on the same side of AB and extend the line formed by joining the two end points of the two perpendicular lines which does not line on the line AB.
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.
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
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
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.
y = -2x+16 which can be expressed in the form of 2x+y-16 = 0
Their values work out as: a = -2 and b = 4
The perpendicular bisector of the straight line joining the two points.
The perpendicular bisector of the line joining the two points.
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
It is the perpendicular bisector of AB, the line joining the two points.
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
They must be equidistant from the point of bisection which is their midpoint and works out that a = -2 and b = 4 Sketching the equations on the Cartesian plane will also help you in determining their values