Question:
The distance from the origin to the image of $(1,1)$ with respect to the line $x + y + 5 = 0$ is:
The distance from the origin to the image of $(1,1)$ with respect to the line $x + y + 5 = 0$ is:
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Using the reflection formula helps determine the image of a point easily.
Updated On: Mar 26, 2025
- $7\sqrt{2}$
- $3\sqrt{2}$
- $6\sqrt{2}$
- $4\sqrt{2}$
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The Correct Option is C
Solution and Explanation
Using the formula for the image of a point $(x_1,y_1)$ with respect to the line $Ax + By + C = 0$:
\[
x' = x_1 - \frac{2A(Ax_1 + By_1 + C)}{A^2 + B^2}, \quad y' = y_1 - \frac{2B(Ax_1 + By_1 + C)}{A^2 + B^2}
\]
Substituting values, we get the image as $(-6,-6)$. The required distance from the origin:
\[
D = \sqrt{(-6 - 0)^2 + (-6 - 0)^2} = \sqrt{36 + 36} = 6\sqrt{2}
\]
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