The equation of the line passing through the points $(1, 2)$ and $(-1, 4)$ is:

Question

Given that $ \cot \left( \frac{A+B}{2} \right) \cdot \tan \left( \frac{A-B}{2} \right) = $, and the equation $ \frac{x}{2} + \frac{y}{3} + \frac{2}{6} - 1 = 0 $, find the area of $ \Delta ABC = 2 $.

Answer 1

Step 1: Find slope Given points: \[ (1,2), \quad (-1,4) \] \[ m = \frac{4 - 2}{-1 - 1} = \frac{2}{-2} = -1 \]

Step 2: Use point-slope form Using point $(1,2)$: \[ y - 2 = -1(x - 1) \] \[ y - 2 = -x + 1 \]

Step 3: Rearrange \[ x + y = 3 \] Thus, the required equation is: \[ {x + y = 3} \]

Economic System	Characteristics
a. Capitalism	i. Private ownership of resources; market-driven economy with minimal government intervention
b. Socialism	ii. Government ownership of key industries; centralized economic planning
c. Mixed Economy	iii. Combination of private and government ownership; focus on social welfare and regulation
d. Market Economy	iv. Private ownership with some government regulation; competition and market forces determine economic outcomes

The equation of the line passing through the points $(1, 2)$ and $(-1, 4)$ is:

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The Correct Option is A

Solution and Explanation

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