# If A=(-4, 3) and B = (8, -6) find length of AB

2
by harjeetsingh

2015-08-10T19:41:44+05:30
Ok, h of a to axix is -4 and other way is 3. Use pythagorean theorem.
4²=16
3²=9
√(16+9)=5
Therefore one height is 5.
Othere sides are 8 and -6
8²=64
6²=36
√(64+36)=10
Therefore the other height is 10.
5+10=15.
Therefore total length is 15.

Ans=15

2015-08-10T19:54:13+05:30
See, the point A on 2nd quadrant makes a rectangle on that quadrant and its length l = 4 unit and breadth is = 3 unit.
As it is a rectangle the length of its diagonal will be calculated according to the formula which is derived from the Pythagoras Theorem that is √(l²+b²)
Let the diagonal be d1
So
d1 = √(4²+3²)
⇒d1=√(16+9)
⇒d1=√25
d1 = 5 units
Now the point B on the fourth quadrant makes which also a rectangle which has length l=8 and breadth b= 6
In the same way we will calculate the diagonal of this rectangle on fourth quadrant
as of Point A.
let the diagonal be d2,
d2=√(l²+b²)
⇒d2=√(8²+6²)
⇒d2=√100
d2 =  10  unit
Now to calculate the length of AB we will join the diagonal d1 and d2 as AB line crosses the the origin and their diagonal touches the origin too.
So, the length AB = d1 + d2 = 10 + 5 = 15  units                                                 Ans.
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