Question

Points $(-2, 4, 7)$, $(3, - 6, - 8)$ and $(1, - 2, - 2)$ are
1) Collinear
2) Vertices of an equilateral triangle
3) Vertices of an isosceles triangle
4) None of the above

Answer 1

Hint: First we need to find the points. Use the slope formula to find the points. Then substitute in the equation to find the values. If the values are the same they are collinear. Because collinear points lie on the same line. finding pointsCollinear points are those that are situated along a single or shared straight line. Collinear points are those that are on a line either close to or far from another point or more than two points.

Formula Used:
The slope formula is
$m=\dfrac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}$

Complete step by step Solution:
If the slope of any two pairs of points is the same, three or more points are said to be collinear. The slope of the line essentially quantifies how steep the line is.
Assume that X, Y, and Z are the three points from which we can create three sets of pairings, resulting in XY, YZ, and XZ being three pairs of points. Consequently, using the slope formula,
The points X, Y, and Z are collinear if the Slope of XY = Slope of YZ = Slope of XY.
The slope formula is
$m=\dfrac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}$
Substitute the values of each point in the given equation
We get
$\dfrac{(3-(-2))}{1-3}=\dfrac{-6-4}{-2-(-6)}=\dfrac{-8-7}{-2-(-8)}$
Which implies the values are
$\Rightarrow-\dfrac{5}{2}=-\dfrac{5}{2}=-\dfrac{5}{2}$

Hence, the correct option is 1.

Note: If two or more points are on the same line, they are said to be collinear in geometry. As a result, the set of points that lie on a single straight line are the collinear points.