Question

verify whether the following points are collinear or not.
A(1,-3),B(2,-5),C(-4,7)​

Answer 1

Let A(1,-3)=(x1,y1), B(2,-5)=(x2,y2), and C(-4,7) = (x3,y3) are three veriticies

of a Triangle ABC .

Area∆ABC

= 1/2|x1(y2-y3)+x2(y3-y1)+x3(y2-y1)|

=1/2|1[-5-7]+2[7-(-3)]+(-4)[-3+5]|

= 1/2| (-12)+2(7+3)+(-4)(-3+5)|

= 1/2| -12 + 2×10 + (-4)(2) |

= 1/2 | -12 + 20 - 8 |

= 1/2 | 20 - 20 |

= 1/2 × 0

= 0

Therefore ,

area ∆ABC = 0 ,

A, B and C are collinear .

I HOPE THIS ANSWER HELPS YOU

Answer 2

The points A(1,-3),B(2,-5),C(-4,7)​ are collinear.

Step-by-step explanation:

Given : The points A(1,-3),B(2,-5),C(-4,7)​.

To find : Verify whether the following points are collinear or not?

Solution :  

When three points are collinear then the condition is  

$x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2) = 0$

Where, $x_1 = 1, x_2 = 2,x_3 = -4, y_1 =-3, y_2 = -5, y_3 = 7$

Taking LHS and substitute the values,

$LHS=1(-5-7) + 2(7-(-3)) +(-4)(-3-(-5))$

$LHS=1(-12) + 2(10) +(-4)(2)$

$LHS=-12+20-8$

$LHS=0$

$LHS=RHS$

Therefore, the points A(1,-3),B(2,-5),C(-4,7)​ are collinear.

#Learn more

Verify that whether the points (1, 5), (2, 3) and (-2, -1) are collinear or not

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