2 Answers

Anjuman · Answer 1 · 2019-05-13T09:05:14+0000

In the given triangle , Coordinates of A (-1,3) , B (-5,-1), C (3,-1).

Let's find the slope of AB and AC .

Formula of slope is

m = (y_(2) - y_(1) )/(x_(2) - x_(1))

For AB, slope is,

m = (-1-3)/(-5+1) = (-4)/(-4) =1

And slope of AC is

(-1-3)/(3+1) = (-4)/(4) = -1

Product of the slopes of AB and AC is

= 1* (-1) =-1

Since the product of the two slopes is -1, so AB and AC are perpendicular.

And if they are perpendicular, angle BAC is 90 degree, so the triangle is right triangle .

Now we check the length of the sides of the triangle, and for that we use distance formula , which is

$d = \sqrt{ (x_(2) - x_(1) )^2 + (y_(2) - y_(1) )^2}$

So for AB,

$AB = √( (-3-1)^2 + (-5+1)^2) = √(32) = 4 \sqrt 2$

For AC,

$AC = √( (-1-3)^2 + (3+1)^2 ) =√(32) = 4 \sqrt 2$

For BC,

√((-1+1)^2 + (3+5)^2 ) = 8

And since two sides are equal, so the triangle is isosceles triangle .

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