Question

Math

Posted 3 months ago

```
Point $Q^{\prime}(3,2)$ is the image of $Q(6,4)$ under a translation.
Determine the translation.
Use non-negative numbers.
A translation by $\square$ units to the right/left $\square$ and $\square$ units
up/down
```

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Answer from Sia

Posted 3 months ago

Solution by Steps

step 1

Identify the original coordinates of point $Q$ and the translated coordinates of point $Q'$

step 2

Calculate the change in the $x$-coordinate from $Q$ to $Q'$ by subtracting the $x$-coordinate of $Q'$ from the $x$-coordinate of $Q$: $6 - 3$

step 3

Calculate the change in the $y$-coordinate from $Q$ to $Q'$ by subtracting the $y$-coordinate of $Q'$ from the $y$-coordinate of $Q$: $4 - 2$

step 4

Determine the direction of the translation for both $x$ and $y$ coordinates based on the signs of the changes calculated in steps 2 and 3

Answer

The translation is 3 units to the left and 2 units down.

Key Concept

Translation in the Coordinate Plane

Explanation

To find the translation that maps point $Q$ to point $Q'$, we subtract the coordinates of $Q'$ from the coordinates of $Q$. The result gives us the magnitude and direction of the translation. A positive result indicates a translation to the right (for $x$) or up (for $y$), while a negative result indicates a translation to the left (for $x$) or down (for $y$). In this case, the translation is to the left and down because the changes in coordinates are negative.

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