Question #209793

1.consider the point a=(-1,0,1), b=(0,-2,3),and c=(-4,4,1) to be vertices of a triangle∆.evaluate all side lengths of ∆.

2.let ∆ be the triangle with vertices the points p=(3,1,-1),q=(2,0,3)and r=(1,1,1).determine whether ∆ is a right angle triangle.if it is not ,explain with reason,why?


1
Expert's answer
2021-06-23T15:13:00-0400

Solution.

1.a=(1;0;1);b=(0;2;3);c=(4;4;1);1. a=(-1;0;1); b=(0;-2;3); c=(-4;4;1);

ab=(0+1)2+(20)2+(31)2=3;ab=\sqrt{(0+1)^2+(-2-0)^2+(3-1)^2}=3;

bc=(40)2+(4+2)2+(13)2=214;bc=\sqrt{(-4-0)^2+(4+2)^2+(1-3)^2}=2\sqrt{14};

ac=(4+1)2+(40)2+(11)2=5;ac=\sqrt{(-4+1)^2+(4-0)^2+(1-1)^2}=5;

2.p=(3,1,1),q=(2,0,3),r=(1,1,1);2. p=(3,1,-1),q=(2,0,3), r=(1,1,1);

pq=(23)2+(01)2+(3+1)2=32;pq=\sqrt{(2-3)^2+(0-1)^2+(3+1)^2}=3\sqrt{2};

pr=(13)2+(11)2+(1+1)2=22;pr=\sqrt{(1-3)^2+(1-1)^2+(1+1)^2}=2\sqrt{2};

qr=(12)2+(10)2+(13)2=6;qr=\sqrt{(1-2)^2+(1-0)^2+(1-3)^2}=\sqrt{6};

If the triangle is right-angled, then the square of the hypotenuse is equal to the sum of the squares of the legs:

pq2=pr2+qr2;pq^2=pr^2+qr^2;

188+6=14,18\not=8+6=14, the triangle is not right-angled.

Answer: 1)3;214;5;1) 3;2\sqrt{14};5;

2)2) A triangle is not right-angled because Pythagoras' theorem does not hold.



Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!
LATEST TUTORIALS
APPROVED BY CLIENTS