(apexvs) if , line jk is parallel to line lm, which of the following statements are true?
a. jk and lm are perpendicular
b. jk and lm lie in the same plane.
c. jk and lm do not lie in the same plane.
d. jk and lm are skew.
e. jk and lm are parallel.
f. jk and lm do not intersect.

We are given that

JK is parallel to line LM

now, we will verify each options

option-A:

we know that when two lines are parallel

they will never intersect

But two perpendicular lines always intersect

so, this is FALSE

option-B:

Two parallel lines can either lines in same plane or different plane as long they do not intersect with each other

so, this is TRUE

option-C:

Two parallel lines can either lines in same plane or different plane as long they do not intersect with each other

so, this is FALSE

option-D:

we know that

Two or more lines which have no intersections but are not parallel.

Since two lines in the plane must intersect or be parallel, skew lines can exist only in three or more dimensions

so, this is FALSE

option-E:

It is already given

so, this is TRUE

option-F:

We know that

parallel lines never intersect

so, this is TRUE

answer: e 9, 5.75

step-by-step explanation:

step 1

find the variation ab in the x coordinate

delta x=(x2-x1)=10-> 8 units

find the variation ab  in the y coordinate 

delta y=(y2-y1)=6-> 2 units

step 2

find the coordinates point c

  x coordinate 

cx=ax+delta x*2/> cx=2+8*(2/> cx=3

  y coordinate 

cy=ay+delta y*2/> cy=4+2*(2/> cy=4.25

the coordinates of point c are (3,4.25)

step 3

find the coordinates point d

  x  coordinate 

dx=ax+delta x*4/> dx=2+8*(4/> dx=4

  y  coordinate 

dy=ay+delta y*4/> dy=4+2*(4/> dy=4.5

the coordinates of point d are (4, 4.5)

step 4

find the coordinates point e

  x  coordinate 

ex=ax+delta x*4/> ex=2+8*(6/> ex=5

  y  coordinate 

ey=ay+delta y*4/> ey=4+2*(6/> ey=4.75

the coordinates of point e are (5, 4.75)

step 5

find the coordinates point f

  x  coordinate 

fx=ax+delta x*4/> fx=2+8*(8/> fx=6

  y  coordinate 

fy=ay+delta y*4/> fy=4+2*(8/> fy=5

the coordinates of point f are (6,5)

step 6

find the coordinates point g

  x  coordinate 

gx=ax+delta x*4/> gx=2+8*(10/> gx=7

  y  coordinate 

gy=ay+delta y*4/> gy=4+2*(10/> gy=5.25

the coordinates of point g are (7,5.25)

step 7

find the coordinates point h

  x  coordinate 

hx=ax+delta x*4/> hx=2+8*(12/> hx=8

  y  coordinate 

hy=ay+delta y*4/> hy=4+2*(12/> hy=5.5

the coordinates of point h are (8,5.5)

step 8

find the coordinates point i

  x  coordinate 

ix=ax+delta x*4/> ix=2+8*(14/> ix=9

  y  coordinate 

iy=ay+delta y*4/> iy=4+2*(14/> iy=5.75

the coordinates of point i are (9,5.75)

- r3ktforgood ☕