Find the points on the line y=3-x which are 2 units from (1,1)

We are tasked with finding the points on the line \( y = 3 - x \) that are exactly 2 units away from the point \( (1,1) \).

### Step-by-step Solution:

#### 1. Equation of the line:
The line is given by:
\[
y = 3 - x
\]
which can also be written as the parametric equation for points on the line:
\[


Discover how to find points on the line y = 3 - x that are exactly 2 units away from the point (1,1) using the distance formula and basic analytic geometry principles. This problem involves key concepts like linear equations and the Pythagorean theorem, suitable for students in Grades 10-12.

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