If the two lines and are perpendicular, then the distance of their point of intersection from the origin is

Question

If the two lines  and  are perpendicular, then the distance of their point of intersection from the origin is

Canvas Classes · Accepted Answer

🧠 Perpendicularity Pins ; Then Solve the 2×2 System for the Intersection

Two lines are perpendicular iff the product of their slopes is . Express both slopes, set product , solve for . Then plug back into the lines and solve for their intersection. Distance from origin is the standard formula.

🗺️ The Clean Algebraic Route

Slope of : .

Perpendicular: .

Factor: . The quadratic has discriminant , so no real roots. The only real root is .

(Sanity check:  — and  qualifies.)

Plu

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