the Orthocenter of the triangle formed by (0, 0), (8, 0), (4, 6) is
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1
Answer:
Correct option is
A
(4,
3
8
)
Let ABC be the given triangie and the vertices be A(0,0),B(8,0) and C(4,6).
∵ Slope of BC=
(4−8)
(6−0)
=−
2
3
.
∴ Equation of line through A and ⊥ to BC is
y−0=(
3
2
)(x−0)⇒2x−3y=0 ...(1)
And slope of CA=
(4−0)
(6−0)
=
2
3
∴ Equation of line through B and ⊥ to CA is
y−0=(−
3
2
)(x−8)⇒2x+3y=16 ...(2)
Solving (1) and (2), the orthocentre is (4,
3
8
).
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