Find the midpoint of PQ with endpoints P(-5, -5) and Q (3, 3). Then write an equation of the line that passes through the midpoint and is perpendicular to PQ. This line is the perpendicular bisector.

The equation of the line that passes through the midpoint and is perpendicular to PQ is

Coordinates of P are  (-5.-5)

Coordinates  of Q are ( 3,3)

The midpoint of the PQ can be found out by the formula given in equation (1)

The midpoint of line joining P and Q we can find out the by putting coordinates in equation (1)

Let O be the mid point of PQ

We can write that the coordinates of O

The slope of line passing through two points  

Slope of line passing through P and Q is given

Let the slope of line that is perpendicular is M

hence the slope M  can be found out in the following way

Let the equation of line passing through point O

(-1,-1) with slope M is given as formulated in equation (2)

Point O (-1,-1) will satisfy the equation of line  

On putting the values of c and M in  equation (2) we get equation of line

So, The equation of the line that passes through the midpoint and is perpendicular to PQ is

For more information please refer to the link given below

link

Step-by-step explanation:

The formula for calculating the midpoint is expressed as:

M(X, Y) = [(x2+x1)/2, (y2+y1)/2]

Given the coordinates P(-5, -5) and Q (3, 3)

Midpoint = [-5+3/2, -5+3/2]

Midpoint = (-2/2, -2/2)

Midpoint = (-1, -1)

Next is to find an equation of the line that passes through the midpoint and is perpendicular to PQ.

The standard form of equation of a line is y = mx+c

Get the slope m:

m = y2-y1/x2-x1

m = 3-(-5)/3-(-5)

m = 8/8

m = 1

For two lines to be perpendicular, the poduct of their slope must be -1

mM = -1

M(1) = -1

M = -1/1

M = -1

To get the slope, substitute the midpoint (-1,-1) and the slope m = -1 into the equation y = mx+c

-1 = -1(-1)+c

-1 = 1+c

c = -1-1

c = -2

Substitute M =-1 and c = -2 into the equation to get the equation of the required line;

y = Mx+c

y = (-1)x-2

y  = x-2

Hence the required equation is y = -x-2

fa tha first one you gonna add y to both sides

it look like this

x-y+y=6+y

x=y+6

therefore your answer is

x =y+6

fa tha second one

you gonna flip tha equation

it gonna look like x-4y=y

then add 4 to both sides

it gonna look like tha

x-4 +4 =y +4

so therefore tha answer is x=y+4

step-by-step explanation:

step-by-step explanation: