Write the equation of the line that passes through the point (1,2) and the midpoint of the line that passes through (2,3) and (2,-5).Write the equation of the line that passes through the point...

Write the equation of the line that passes through the point (1,2) and the midpoint of the line that passes through (2,3) and (2,-5).

Write the equation of the line that passes through the point (1,2) and the midpoint of the line that passes through (2,3) and (2,-5).

Asked on by leeaeel

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hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

The line passes through :

A ( 1, 2)

and B(xB, yB) where B is midpoint of (2,3) and (2,-5)

Let us find B:

xB = (2+2)/2 = 2

yB = 3+-5/2 = -2/2 = -1

Then the point B (2,-1)

Now we have A and B passes through the line:

==> y-yA = m(x-xA)

m = (yB-yA)/(xB-xA) = (-1-2)/(2-1) = -3

==> y-2 = -3(x-1)

==> y-2 = -3x + 3

==> y= -3x + 5

william1941's profile pic

william1941 | College Teacher | (Level 3) Valedictorian

Posted on

The mid point of (2,3) and (2,-5) is [(2+2)/2, (3-5)/2] or (2, -1)

The other point we are given is (1, 2)

So we need the equation of the line that passes through (2, -1) and (1, 2) .

We know that the equation of the line through ( x1, y1) and (x2, y2) is given by: y-y1 = [(y2-y1)/(x2-x1)]*(x-x1)

Here, substituting the values we get:

y-(-1)= [(2- (-1))/(1- 2)]*(x- 2)

=> y+1 = [(2+1)/-1]* (x-2)

=> y+1 = -3 (x-2)

=> y+1 = -3x + 6

=> 3x + y - 5 = 0

So the required equation is 3x + y - 5 = 0

 

neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

The equation of the line passing through (x1,y1) and (x2,y2) is given by"

y-y1 = {(y2-y1)/(x2-x1)} (x-x1).

Therefore (x1 ,y1) = (2,3) and (x2,y2) = (2,-5) . Here x2-x2 = 0. So , we can write the equation:

(x-x1) = ((X2-x1)/(y2-y1)}(y-y1)

x-2 =  {(2-2)/(-5-3)(y--3)

x-2 = 0*(y-3)/-8 = 0

 Sox-2 = 0 Or x= 0 is the equation of the line.

 

 

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We'll determine the coordinates of the midpoint of the line that passes through the points (2,3) and (2,-5).

xM=(x2+x1)/2=(2+2)/2=2

yM= (y2+y1)/2=(3-5)/2=-1

In order to write the equation of the line that passes through the points N (1,2) and M(2,-1), we have to determine the slope of this line mMN = (yM-yN)/(xM-xN)

mMN = (-1-2)/(2-1)

mMN = -3

The equation of the line that passes through the points MN IS:

y-yN=mMN*(x-xN)

y-2=(-3)*(x-1)

We'll remove the brackets:

y-2+3x-3=0

y+3x-5=0

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