Determine the coordinates of the point where the line through the points A(2, 3, 2) and B(5, 1, 6) crosses the XY -plane. - Mathematics MCQ Mathematics Mock Test - 9 2026 | ExamTest.live

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Determine the coordinates of the point where the line through the points A (2, 3, 2) and B (5, 1, 6) crosses the X Y -plane.

Solution & Step-by-step Explanation

Equation of line passing through (2, 3, 2) and (5, 1, 6) : \frac{x - 2}{5 - 2} = \frac{y - 3}{1 - 3} = \frac{z - 2}{6 - 2} \frac{x - 2}{3} = \frac{y - 3}{- 2} = \frac{z - 2}{4} = λ Any point on the line is (3 λ + 2, - 2 λ + 3, 4 λ + 2) .At the X Y -plane, z = 0 . 4 λ + 2 = 0 ⟹ λ = - 1/2 .Coordinates: x = 3 (- 1/2) + 2 = - 3/2 + 2 = 1/2 y = - 2 (- 1/2) + 3 = 1 + 3 = 4 z = 0 Point is (1/2, 4, 0) .

Try it yourself before checking the explanation above.

Determine the coordinates of the point where the line through the points A (2, 3, 2) and B (5, 1, 6) crosses the X Y -plane.

(7/2, 4, 1/2)

(3/2, 4, 2)

(7/2, 2, 0)

(1/2, 4, 0)

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