065. Intersection of Two Lines

Codeforces

IDCF10269065

Time1000ms

Memory256MB

Difficulty—

English · Original

Formal · Original

When performing calculations on linear equations, finding the intersection point of two lines is a very common task. Write a program that takes two linear equations in the form of $y = m x + b$ and outputs the $x$ coordinate at which the two lines intersect. The first line contains two floating point values representing the $m$ and $b$ values of the first linear equation respectively. The second line contains the two variables corresponding to the $m$ and $b$ variables of the second linear equation. A single floating point value that represents the $x$ coordinate at which the two lines intersect. Assume that all test cases contain lines that do intersect. ## Input The first line contains two floating point values representing the $m$ and $b$ values of the first linear equation respectively. The second line contains the two variables corresponding to the $m$ and $b$ variables of the second linear equation. ## Output A single floating point value that represents the $x$ coordinate at which the two lines intersect. [samples] ## Note Assume that all test cases contain lines that do intersect.

**Definitions** Let $ m_1, b_1 \in \mathbb{R} $ be the slope and y-intercept of the first line. Let $ m_2, b_2 \in \mathbb{R} $ be the slope and y-intercept of the second line. **Constraints** 1. $ m_1 \neq m_2 $ (lines intersect at exactly one point). **Objective** Find the $ x $-coordinate of the intersection point: $$ x = \frac{b_2 - b_1}{m_1 - m_2} $$

API Response (JSON)

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