8. The two vertices of a right-angled triangle ABC, right-
angled at A are A(2, 4) and B(6, 4). Plot these two
points on a Cartesian plane and find the coordinates
of the possible points C, given that the height of the
triangle ABC is 5 units.
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Answer:
Let the points be A(2,2),B(2,1),C(5,2).
Distance between two points (x
1
,y
1
) and (x
2
,y
2
) can be calculated using the formula
(x
2
−x
1
)
2
+(y
2
−y
1
)
2
Hence, Length of side AB =
(−2−2)
2
+(1+2)
2
=
16+9
=
25
=5
Length of side BC ==
(5+2)
2
+(2−1)
2
=
49+1
=
50
Length of side AC =
(5−2)
2
+(2+2)
2
=
9+16
=
25
=5
Since, (
50
)
2
=(
25
)
2
+(
25
)
2
,
=>BC
2
=AB
2
+AC
2
Hence, the triangle has a right angle at A, with AB and AC as base and height.
Area of the triangle ABC =
2
1
×base×height=
2
1
×5×5=
2
25
sq units.
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