Show that the points A(3.-5), B(4,3) & C(11.-4) are the vertices of an isosceles triangle. 3. In the given figure, points B & C lie on tangent to the circle drawn at point A
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Class 11
>>Applied Mathematics
>>Straight lines
>>Introduction
>>Prove that the points (7,10),( - 2,5) an
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Prove that the points (7,10),(−2,5) and (3,−4) are the vertices of an isosceles right triangle.
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Let the vertices of an isosceles right triangle be A(7,10), B(-2,5) and C(3,-4)
So by distance formula we have,
Distance between two points =
(x
2
−x
1
)
2
+(y
2
−y
1
)
2
AB=
(−2−7)
2
+(5−10)
2
=
81+25
=
106
BC=
(3+2)
2
+(−4−5)
2
=
(25+81)
=
106
AC=
(3−7)
2
+(−4−10)
2
=
−16+196
=
212
∴AB=BC⇒ This implies that ABC is an isosceles triangle.
Also,
AB
2
+BC
2
=106+106=212
∴AB
2
+BC
2
=AC
2
(Pythagoras theorem)
Hence, proved
∴ Δ ABC is a right triangle (proved)