Given A(-1,4) and B(3,-2). A .Find the length AB B .Find the midpoint of segment

Question

Given A(-1,4) and B(3,-2).

A.Find the length AB

B.Find the midpoint of segment AB

C.Find the coordinates of Cif A is the midpoint of segment BC

D.Find the equation of the line through A and B in:

i. Slope intercept form (y=mx+b)

ii. General form with Integer coefficients (Ax+By=C or Ax+By+C=0)

E.Find the coordinates of all points on the y-axis that are 5 units from B

F.Find the equation of the line parallel to line AB through the (1,0).

G.Find the equation of the line through the (4,2) perpendicular to line AB

Explanation / Answer

A. AB=sqrt((3-(-1))2+(-2-4)2) =sqrt(16+36) =sqrt52=2sqrt 13

B. Midpoint of AB=((-1+3)/2,(-2+4)/2) = (1,1)

C. Let the coordinate of C =(x,y)

-1=(x+3)/2 , 4=(y-2)/2

x=-5 , y=10

point is (-5,10)

D. slope=(-2-4)/(3+1)=-6/4=-3/2

y=mx+b

4=(-3/2)(-1)+b

b=5/2

y=(-3/2)x +5/2

ii. In general form

2y=-3x+5

3x+2y=5

E. On y axis means x=0

Five units from B means (0,-2-5) ,(0(-2+5) =(0,-7),(0,3)

F. slope of AB=-3/2

Therefore slope of required line =-3/2

y=mx+b

0=(-3/2)(1)+b

b=3/2

y=(-3/2)x +(3/2)

G. Slope of AB=-3/2

Therefore slope of required line =2/3

y=mx+b

2=(2/3)(4)+b

b=-2/3

y=(2/3)x -2/3

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