Question

After a translation the image of A(-6,-2) is B(-4,-4). What is the image of the point C(3,-1) after this translation?

A. (-5,1)
B.(5,-3)
C.(5,1)
D.(-5,-3)

Answer 1

Answer: B.(5,-3)

===========================================================

Step-by-step explanation:

The preimage (-6,-2) shifts to the image point (-4,-4)

Focus on the x coordinates. The jump from -6 to -4 is an increase of 2. So we have x become x+2

Now focus on the y coordinates. The jump from -2 to -4 is -2, so y becomes y-2

The translation rule we use is
`(\text{x},\text{y})\to (\text{x}+2,\text{y}-2)` which shifts the point 2 units to the right and 2 units down.

-----------------

Let's apply this rule to the point (3,-1)

`(\text{x},\text{y})\to (\text{x}+2,\text{y}-2)\\\\(3,-1)\to (3+2,-1-2)\\\\(3,-1)\to \boldsymbol{(5,-3)}\\\\`

The preimage (3,-1) shifts to the image (5, -3)