Question Find the image coordinates of a point $Q(-5,1)$ under the transformation $(x, y) \rightarrow(-y,-x)$ .

Studdy Solution

STEP 1

Assumptions
1. The preimage coordinate is $Q(-5,1)$ .
2. The transformation is described by the coordinate notation $(x, y) \rightarrow(-y,-x)$ .
3. We need to apply the transformation to the preimage to find the image coordinate $Q'$ .

STEP 2

Identify the components of the preimage coordinate.
The preimage coordinate is $Q(-5,1)$ , where $x = -5$ and $y = 1$ .

STEP 3

Apply the transformation to the preimage coordinate.
The transformation $(x, y) \rightarrow(-y,-x)$ tells us to replace $x$ with $-y$ and $y$ with $-x$ .

STEP 4

Substitute the values of $x$ and $y$ from the preimage into the transformation.
For $Q(-5,1)$ , we have $x = -5$ and $y = 1$ . Applying the transformation:
$(-y,-x) = (-(1),-(-5))$

STEP 5

Calculate the new coordinates after applying the transformation.
$(-y,-x) = (-1,5)$

STEP 6

Write down the coordinates of the image $Q'$ .
The image coordinate after the transformation is $Q'(-1,5)$ .
Therefore, the correct answer is $Q^{\prime}(-1,5)$ .

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