Question

What is the image of left bracket, minus, 12, comma, 4, right bracket(−12,4) after a dilation by a scale factor of one quarter

4
1
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centered at the origin?

Answer 1

Dilate (-4, 12) by 1/4 to get (-1, 3). Reflecting across the origin yields the final image: (1, -3).

let's break down the solution step by step:

1. Dilation:

The dilation factor is 1/4. To dilate the coordinates (-4, 12), multiply each coordinate by the dilation factor:

`\[ \text{Dilated coordinates} = \left((1)/(4) * (-4), (1)/(4) * 12\right) = (-1, 3) \]`

2. Reflection across the Origin:

To form the image across the origin, negate both coordinates of the dilated point:

`\[ \text{Image across the origin} = -(-1, 3) = (1, -3) \]`

Therefore, the required image of the given point (-4, 12) with a dilation factor of 1/4 and centered at the origin is (1, -3).

Que. What is the image of (-4,12) after a dilation by a scale factor of 1/4 centered at the origin.