Question

class IX math 1) k এর মান কত হলে (১,-১), (২,-১), এবং (k,-১) বিন্দুত্রয় একই সরল রেখায় থাকবে?​

Answer 1

k =0.

• Points that are on the same straight line are referred to as collinear points. They must lie on the same straight line, even if they don't have to be co-planar. The Latin terms "col" and "linear," where "col" means "together" and "linear" means "in the same line," are the source of the English word "colinear." Collinearity is the state of being shared by two points.
• A group of three or more points that are located along the same straight line are called collinear points. On separate planes, collinear points may exist, but not on different lines. Collinearity is the quality of two points being parallel to one another. Any three or more points are only considered to be collinear if they are situated along the same straight line. There is only one line that can pass through three locations that are collinear.

Here, the points are given as,

(1,-1), (2,-1) and (k,-1)

Let $x_{1}$ = 1, $y_{1}$ = -1, $x_{2}$ = 2, $y_{2}$ = -1, $x_{3}$ = k, $y_{3}$ = -1.

Now, the points will be collinear if,

$x_{1}(y_{2}-y_{3)}+x_{2}(y_{3}-y_{1})+x_{3}(y_{1}-y_{2})=0$

Or, 1(-1+1) + 2(-1+1)+k(-1+1) = 0

Then, k = 0.

Hence, k =0.

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Answer 2

Answer:

For 'k' belonging to real number the point will make a straight line .

Explanation:

What is a Straight Line ?

A line is a geometry object that extends on both sides and is defined by zero width. Simply said, a straight line is a line devoid of bends. A straight line is one that has no bends and continues to infinity on both sides.

The following is the generic equation for the straight line:

ax + by + c = 0

a b, and c are constants where x and y are variables.

The slope-intercept version of the equation for a straight line is as follows:

y = mx + c

Here, m stands for the line's slope and c for its y-intercept.

Slope of the line formed by (1, -1) and (2,-1) is

$\frac{-1-(-1)}{2-1} = \frac{-1+1}{1} = 0$

Equation of the line is :

y = mx + c

⇒ y = c                      [∵ slope (m) = 0]

from the point (1,-1)

c = -1

So ,Equation of the line is

y = -1.

So for any real value of k the equation is satisfied.

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