Question

prove that 4, 4 3, 5 and -1, -1 are the vertices of a right angle triangle​

Answer 1

I'm assuming that you have shared the coordinates for the vertices.


So if that traingle is right angles it must follow pythagoras theorem.

Let's find the length of the sides first,

Side 1:

$\sqrt{ {4}^{2} + {4}^{2} } = \sqrt{32} = 4 \sqrt{2}$

Side 2:

$\sqrt{ {3}^{2} + {5}^{2} } = \sqrt{34}$

side 3:

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


As we can see the largest side is 3,
and if it were a right angled triangle it would be this side that would make up the hypotaneous,

So,

Applying Pythagoras theorem now,
${(4 \sqrt{2} )}^{2} + { (\sqrt{2}) }^{2} \\ = 32 + 2 \\ = 34 = third \: side \: squared$

Therefore it is a right angled traingle.

Answer 2

Step-by-step explanation:

i hope this answers is helpful for you