Question

Show that the points (1, 4); (3, -2) and (-3, 16) are Collinear

Answer 1

Answer:

Electromagnetism is a branch of physics involving the study of the electromagnetic force, a type of physical interaction that occurs between electrically charged particles. ... At high energy, the weak force and electromagnetic force are unified as a single electroweak force.

Answer 2

Step-by-step explanation:

Given :-

(1, 4); (3, -2) and (-3, 16)

To find:-

Show that the points (1, 4); (3, -2) and (-3, 16) are Collinear Points .

Solution:-

Given points are (1, 4); (3, -2) and (-3, 16)

Let (x1, y1) = (1,4) => x1 = 1 and y1 = 4

Let (x2, y2) = (3,-2) => x2 = 3 and y2 = -2

Let (x3, y3) = (-3,16) => x3 = -3 and y3 = 16

We know that

If the points A(x1, y1) ,B(x2, y2) and C(x3, y3) are collinear points then the area of the triangle formed by the points is Zero

Area of a triangle =

∆= (1/2)|x1(y2-y3)+x2(y3-y1)+x3(y1-y2) | sq.units

On Substituting these values in the above formula

=> (1/2) | (1)(-2-16) +(3)(16-4) +(-3)(4-(-2)) |

=> (1/2) | (1)(-18)+(3)(12)+(-3)(6) |

=> (1/2) | -18+36-18 |

=> (1/2) | 36-36 |

=> (1/2) | 0 |

=> (1/2)×0

=> 0/2

=> 0

Area of the triangle formed by the given points is zero

They are Collinear points.

Hence, Proved.

Answer:-

The given points (1, 4); (3, -2) and (-3, 16) are Collinear Points.

Used formulae:-

Area of a triangle formed by the points A(x1, y1) ,B(x2, y2) and C(x3, y3) is given by ∆ =

(1/2)|x1(y2-y3)+x2(y3-y1)+x3(y1-y2) | sq.units

Used Concept:-

If three points are Collinear points then the area of the triangle formed by the points is equal to zero (0)