* Determine whether each of the given points (-2, 1), (2,-2) and
(52) are the vertices of right angle.
Answers
Answered by
0
Answer:
25
Step-by-step explanation:
Proof:
By distance formula,
AB=
(−2−2)
2
+(1+2)
2
=
16+9
=
25
=5
BC=
(−2−5)
2
+(1−2)
2
=
(−7)
2
+(−1)
2
=
50
=5
2
Length of the hypotenuse
AC=
(5−2)
2
+(2+2)
2
=
(3)
2
+(4)
2
=
25
∴AB
2
+AC
2
=25+25=50=BC
2
∴ △ ABC is a right-angled triangle
Area of the triangle ABC
=
2
1
[x
1
(y
2
−y
3
)+x
2
(y
3
−y
1
)+x
3
(y
1
−y
2
)]sq.
Area of the △ABC
=
2
1
×Base×height
=
2
1
×5×5
=
2
25
sq.units.
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