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Given points P(2,3), Q(4, -2), and R(alp...

Given points `P(2,3), Q(4, -2), and R(alpha,0)`. Find the value of a if `PR + RQ` is minimum.

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To find the value of \( \alpha \) such that the sum of distances \( PR + RQ \) is minimized, we will follow these steps: ### Step 1: Write the distance formulas The distance \( PR \) between points \( P(2, 3) \) and \( R(\alpha, 0) \) can be calculated using the distance formula: \[ PR = \sqrt{(\alpha - 2)^2 + (0 - 3)^2} = \sqrt{(\alpha - 2)^2 + 9} \] ...
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