The reflection of the origin in the plane P_2 : 2x + 3y + 4z + 5 = 0 is: - Mathematics MCQ Mathematics Mock Test - 11 2026 | ExamTest.live

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The reflection of the origin in the plane P_{2} : 2 x + 3 y + 4 z + 5 = 0 is:

Solution & Step-by-step Explanation

Let the reflection of the origin (x_{1}, y_{1}, z_{1}) = (0, 0, 0) in the plane a x + b y + cz + d = 0 be (x, y, z) .The formula for reflection is: \frac{x - x _{1}}{a} = \frac{y - y _{1}}{b} = \frac{z - z _{1}}{c} = - 2 \frac{( a x _{1} + b y _{1} + c z _{1} + d )}{a ^{2} + b ^{2} + c ^{2}} Here a = 2, b = 3, c = 4, d = 5 and (x_{1}, y_{1}, z_{1}) = (0, 0, 0) . \frac{x - 0}{2} = \frac{y - 0}{3} = \frac{z - 0}{4} = - 2 \frac{( 0 + 0 + 0 + 5 )}{2 ^{2} + 3 ^{2} + 4 ^{2}} \frac{x}{2} = \frac{y}{3} = \frac{z}{4} = - 2 \frac{5}{4 + 9 + 16} = - \frac{10}{29} x = 2 \times (- \frac{10}{29}) = - \frac{20}{29} y = 3 \times (- \frac{10}{29}) = - \frac{30}{29} z = 4 \times (- \frac{10}{29}) = - \frac{40}{29} The reflection is (- \frac{20}{29}, - \frac{30}{29}, - \frac{40}{29}) .

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The reflection of the origin in the plane P_{2} : 2 x + 3 y + 4 z + 5 = 0 is:

(- \frac{20}{29}, - \frac{30}{29}, - \frac{40}{29})

(\frac{20}{29}, \frac{30}{29}, \frac{40}{29})

(- \frac{20}{29}, \frac{30}{29}, - \frac{40}{29})

(\frac{20}{29}, - \frac{30}{29}, \frac{40}{29})

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