Determine whether the following points are collinear. R(1, -4), S(-2, 2), T(-3, 4)
Determine whether the following points are collinear. R(1, -4), S(-2, 2), T(-3, 4)
R(1, –4), S(–2, 2), T(–3, 4)
\[\text { Slope of RS } = \frac{2 - \left( - 4 \right)}{- 2 - 1} = \frac{6}{- 3} = - 2\]
\[\text {Slope of ST} = \frac{4 - 2}{- 3 - \left( - 2 \right)} = \frac{2}{- 1} = - 2\]
Slope of RS = Slope of ST
So, the given points are collinear.
Explanation:-
Given three points R(1, -4), S(-2, 2), and T(-3, 4), we can find the slope of the line segment RS and the slope of the line segment ST using the slope formula.
The slope of the line segment RS is:
slope of RS = (y2 – y1)/(x2 – x1) = (2 – (-4))/(-2 – 1) = 6/-3 = -2
Similarly, the slope of the line segment ST is:
slope of ST = (y2 – y1)/(x2 – x1) = (4 – 2)/(-3 – (-2)) = 2/-1 = -2
We can see that both slopes are equal and negative. This means that the line segments RS and ST are parallel to each other, and they have the same steepness. Therefore, the three points R, S, and T lie on the same line, and they are collinear.
Hence, we can conclude that the given points R(1, -4), S(-2, 2), and T(-3, 4) are collinear.
Chapter 5. Co-ordinate Geometry – Practice Set 5.3 (Page 121)