To determine the translation that maps point $C(-2, -3)$ to its image $C'(-4, -3)$, we use the translation formula:

$(x', y') = (x + a, y + b)$

where $(x, y)$ is the original point, $(x', y')$ is the translated point, and $(a, b)$ represents the translation vector.

Step 1: Find the translation vector

• The change in the $x$-coordinate:
  $a = x' - x = -4 - (-2) = -4 + 2 = -2$
• The change in the $y$-coordinate:
  $b = y' - y = -3 - (-3) = -3 + 3 = 0$

Thus, the translation vector is $(-2, 0)$.

Step 2: Convert to Non-Negative Numbers

Since the translation vector $(-2, 0)$ contains a negative number, we can express the movement using non-negative values:

• A shift of 2 units to the left is the same as a shift of 2 units to the right in the negative direction.
• The movement in the $y$-direction is 0, meaning there is no vertical shift.

Thus, the transformation can be described as:

• A translation of 2 units left.

Would you like further details or another explanation?

Related Questions:

1. What is the translation that maps $A(3,5)$ to $A'(7,2)$?
2. How do you describe a translation using vectors?
3. What is the general formula for translation in the coordinate plane?
4. How do you find the image of a point under a given translation?
5. How do translations relate to reflections and rotations?

Tip:

A translation does not change the shape or size of a figure, only its position.