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Home » y - 5 = 2(x - 2) - Coaching Toolbox

y - 5 = 2(x - 2) - Coaching Toolbox

📅 May 3, 2026 👤 scraface

May 03, 2026

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📌 The reflection of point $ A = (3, -4) $ over the horizontal line $ y = 2 $:

📌 Since the vertical distance from $ A $ to the line is $ 2 - (-4) = 6 $, the reflected point $ A $ lies 6 units above $ y = 2 $, so at $ y = 8 $. Thus, $ A = (3, 8) $.

📌 Then, the reflection law implies that the straight line from $ O = (0,0) $ to $ A = (3,8) $ intersects the line $ y = 2 $ at the optimal point $ P $.

📌 The parametric equation of line $ OA $ is:

📌 Alternatively, verify the reflection condition:

📌 Question: A zoologist is tracking a lemur leaping between two trees in Madagascar. The lemur jumps from point $ P = (1,2) $ to point $ Q = (7,10) $, but there is a high grass patch modeled as the line $ y = x $. To minimize exposure to predators, the lemur aims to land as close as possible to point $ R = (4,4) $ after the jump. Find the point $ L $ on the line $ y = x $ that minimizes the distance from $ L $ to $ R $.

📌 Solution: We seek the point $ L = (a, a) $ on the line $ y = x $ that minimizes the distance to $ R = (4,4) $. The squared distance is:

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