2. Show that the points (2,3,5),(-1,5,- 1) and (4,-3, 2) form a right angled isosceles triangle.
Answers
Given: The points of the triangle (2,3,5), (-1,5,- 1) and (4,-3, 2).
To find: Show that the points form a right angled isosceles triangle.
Solution:
- Now we have given the points: A(2,3,5), B(-1,5,- 1) and C(4,-3, 2).
- Let ABC be the triangle where AB be height, BC be hypotenuse and AC be base.
- Now the length will be:
AB = √(2+1)²+(3-5)²+(5+1)²
AB = √9+4+36
AB = √49
AB = 7
- Similarly :
BC = √(-1-4)²+(5+3)²+(-1-2)²
BC = √25+64+9
BC = √98
- Similarly :
AC = √(4-2)²+(-3-3)²+(2-5)²
AC = √4+36+9
AC = √49
AC = 7
- So now, we can see that
AB² + BC² = AC²
Answer:
So therefore, ABC is right angled isosceles triangle.
Answer:
Proof is given Below...
Step-by-step explanation:
Now we have given the points: A(2,3,5), B(-1,5,- 1) and C(4,-3, 2).
Let ABC be the triangle where AB be height, BC be hypotenuse and AC be base.
Now the length will be:
AB = √(2+1)²+(3-5)²+(5+1)²
AB = √9+4+36
AB = √49
AB = 7
Similarly :
BC = √(-1-4)²+(5+3)²+(-1-2)²
BC = √25+64+9
BC = √98
Similarly :
AC = √(4-2)²+(-3-3)²+(2-5)²
AC = √4+36+9
AC = √49
AC = 7
So now, we can see that
AB² + BC² = AC²
Answer:
Therefore, ABC is right angled isosceles triangle.