Mary is traveling to Ecuador for her summer vacation. She looks at a map of the path of her flight. Her plane leaves from Florida, located at (1, 4) on the map’s coordinate grid, makes a stop at the midpoint, Panama, located at (5, 7 ) on the map’s coordinate grid. and then heads to its destination, Ecuador. Find the location of Ecuador on Mary’s map. Group of answer choices (3, 5.5) (8, 9) (0, 0) (9, 10)

(9, 10)

Step-by-step explanation:

We are told that the coordinates of Mary's departure location is (1,4)

Now, we are told that She stopped at the midpoint of the journey located at Panama with a coordinate of (5, 7).

Now, we want to find the coordinates of her final destination.

Let the coordinates of her final destination be (x, y)

Since midpoint is at (5,7) and the initial point is at (1,4), then to get x;

(x + 1)/2 = 5

x + 1 = 5 × 2

x + 1 = 10

x = 10 - 1

x = 9

Similarly, to get y;

(y + 4)/2 = 7

y + 4 = 14

y = 14 - 4

y = 10

Thus, the coordinates of her final destination is; (9, 10)

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

1e+27

step-by-step explanation: