Question

can a line be drawn between point 1, 2, and 3?
only bewteen 1 and 2
yes
no
only between 2 and 3

Explanation:

Step1: Understand the nature of lines

A line can be drawn through any two points. But the question is about whether a single line can pass through all three points (Point 1, Point 2, and Point 3).

Step2: Check collinearity

Collinear points lie on the same straight - line. If we assume the coordinates of the points (let's say for simplicity, assume a grid where each square is 1 unit. Suppose Point 1 is \((- 4,4)\), Point 2 is \((2,-1)\), Point 3 is \((3,-2)\)).
The slope formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Slope between Point 1\((x_1=-4,y_1 = 4)\) and Point 2\((x_2 = 2,y_2=-1)\) is \(m_{12}=\frac{-1 - 4}{2+4}=\frac{-5}{6}\).
Slope between Point 2\((x_1 = 2,y_1=-1)\) and Point 3\((x_2=3,y_2=-2)\) is \(m_{23}=\frac{-2 + 1}{3 - 2}=-1\).
Since \(m_{12}
eq m_{23}\), the three points are not collinear.

Answer:

No