The figure shows a pair of parallel line segments on a coordinate grid: The line segments are translated 2 units to the left to form E′F′ and G′H′. Which statement describes E′F′ and G′H′? (1 point)

a
Line segments E′F′ and G′H′ intersect at (−2, 0) and are two times farther apart than EF and GH.

b
Line segments E′F′ and G′H′ intersect at (0, −2) and are two times farther apart than EF and GH. .

c
Line segments E′F′ and G′H′ do not intersect and are the same distance apart as EF and GH.

d
Line segments E′F′ and G′H′ do not intersect and are closer together than EF and GH.

C

Step-by-step explanation:

translate 2 units to the left only means they are shifted to the left by 2 units nothing else changed

Topic: coordinate geometry

If you like to venture further, do check out my insta (learntionary) where I constantly post math tips! Thanks!

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12