Question

If the points (a, b), (c,
d.and (a-c , b-d) are collinear, show that ad=bc

Answer 1

Step-by-step explanation:

Given : If the points (a, b), (c, d) and (a-c , b-d) are collinear.

To find : Show that ad=bc ?

Solution :

If three points are collinear then the slope of the line joining any 2 points must be identical.

So, Let X=(a,b) , Y=(c,d) and Z=(a-c , b-d)

Then Slope of XY=Slope of YZ

i.e. $\dfrac{d-b}{c-a}=\dfrac{b-d-d}{a-c-c}$

$\dfrac{d-b}{c-a}=\dfrac{b-2d}{a-2c}$

Cross multiply,

$(a-2c)(d-b)=(b-2d)(c-a)$

$ad-2cd-ba+2bc=bc-ab-2dc+2ad$

$2bc-bc=2ad-ad$

$bc=ad$

Hence showed.

#Learn more

Show that points (a,b+c),(b,c+a),(c,a+b) are collinear

https://brainly.in/question/1509782

Answer 2

Answer:

This is the brilliance answer