Question

What is the component form of the vector that maps XF to X’F’ ?

Answer 1

Answer: <-6, -5> (choice B)

Step-by-step explanation:

The point X is at (5,4) while X' is at (-1, -1)

To move from X to X', we translate 6 units to the left and 5 units down.

So the rule is (x,y) --> (x-6, y-5) which can be written as the translation vector <-6, -5>, as its a shorter notation format.

The same idea is applied to go from F to F'

point F is at (1,2). Let's apply the translation rule to shift (1,2) 6 units to the left and we get to (-5, 2). Now shift 5 units down and we arrive at (-5, -3) which is where F' is located. This helps confirm we have the proper vector.

Answer 2

`\large\boxed{B.\ \left<-6,\ -5\right>}`

Step-by-step explanation:

Look at the picture.

METHOD 1:

Read it from the graph

`\left<-6,\ -5\right>`

METHOD 2:

Calculate it:

`X=(5,\ 4),\ X'(-1,\ -1)\\\\\left<-1-5,\ -1-4\right>=\left<-6,\ -5\right>`