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The key stages of the work are the following:

1) Find the slope for the line that joins the given points.

2) Divide -1 by this slope to get the slope of the perpendicular line.

3) Find the midpoint (calculate the averages of the x-coordinates and of the y-coordinates).

4) Use the point-slope equation of the line to find a line with the desired slope, that goes through the desired point.

Another Answer:-

Points: (-7, -3) and (-1, -4)

Mdpoint: (-4,-3.5)

Slope: -1/6

Perpendicular slope: 6

Equation: 6y = -x-25 or as x+6y+25 = 0

Perpendicular bisector equation: y = 6x+20.5 or as 6x-y+20.5 = 0

Q: What is the equation and its perpendicular bisector equation of the line joining the points of -7 -3 and -1 -4 on the Cartesian plane showing key stages of work?

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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

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 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

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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

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.

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

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

It is the perpendicular bisector of AB, the line joining the two points.

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