Question

show that (4,4),(3,5),(-1,-1) form a right angle triangle ​

Answer 1

Answer:

ANSWER

Let, A(4,4), B(3,5), C(−1,−1).

Lets find slopes of lines AB,AC,BC

We have the slope point form, slope, m=

x

2

−x

1

y

2

−y

1

for tow points (x

1

,y

1

),(x

2

,y

2

)

∴Slope of AB=

3−4

5−4

=−1

Slope of AC=

−1−4

−1−4

=1

Slope of BC=

−1−3

−1−5

=

2

3

We know that, if the product of the slopes of two lines is equal to −1, then the lines are perpendicular to each other.

Here, Slope of AB × slope of AC = −1

∴AB is perpendicular to AC and ∠A=90

∘

Hence the given triangle is right angled