If the scale factor used was k and the perimeter of the pink trapezoid was p, what would the perimeter of the blue trapezoid be?

kP

Step-by-step explanation:

We assume the dimensions of the blue trapezoid are those of the pink trapezoid multiplied by k. If each of the sides is multiplied by k, their sum, the perimeter, is multiplied by k. (The distributive property tells you that.)

... (s1 +s2 +s3 +s4) = P

... (k·s1 +k·s2 +k·s3 +k·s4) = k(s1 +s2 +s3 +s4) = kP

Caveat

We cannot tell from the description which trapezoid is the reference, and which is the one that is the reference multiplied by k. If the above is a wrong guess, then the perimeter is P/k.

  q

step-by-step explanation:

each line from a vertex to the midpoint of the opposite side is called a median. the point where the medians intersect, point q, is the centroid.

the centroid of δabc is point q.

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