Question

Are (1, 2), (-3, 4), (7,- 1) these points form a straight line?​

Answer 1

Answer:

if they form a straight line, a triangle with these points will have area = 0

1/2|1(4+1)+(-3)(-1-2)+7(2-4)|= 0

5 + 9 - 14 = 0

14 - 14 = 0

0 = 0

As L.H.S = R.H.S,

the points form a straight line.

Answer 2

Yes, the points (1, 2), (-3, 4), (7,- 1) form a straight line.

Step-by-step explanation:

The given points are  (1, 2), (-3, 4), (7,- 1).

Concept that we'll use to solve the question:

Find the equation of line passing through any two points and then check if the third point satisfy the equation or not.

Equation of line through  (1, 2), (-3, 4).

Slope of the line is given by

$m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{4-2}{-3-1}\\\\m=\frac{2}{-4}\\\\m=-\frac{1}{2}$

Equation of point slope form is

$y=y_1=m(x-x_1)\\\\y-2=-\frac{1}{2}(x-1)\\\\y-2=-\frac{1}{2}x+\frac{1}{2}\\\\y=-\frac{1}{2}x+\frac{5}{2}$

Substitute x = 7 and y = -1 in this equation

$-1=-\frac{1}{2}\cdot7+\frac{5}{2}\\\\-1=\frac{-7+5}{2}\\\\-1=\frac{-2}{2}\\\\-1=-1=>\text{ True}$

Since, the point satisfy the equation. hence, this point must lie in this line.

Therefore, we can conclude that the points (1, 2), (-3, 4), (7,- 1) form a straight line.

Please see the attached graph which proves this statement as well.

#Learn More:

Write the equation of a line in slope-intercept form given: Slope= -1/2 and a point on the line (6,4).

https://brainly.in/question/6246977