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Byju's Answer
Standard XII
Mathematics
Equation of a Line Passing through Two Given Points
Write the coo...
Question
Write the coordinates of the orthocentre of the triangle formed by points (8, 0), (4, 6) and (0, 0).
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Solution
The intersection point of three altitudes of a triangle is called orthocentre.
In the figure, two altitudes ON and BM of
∆
OAB are shown.
Slope of AB =
6
-
0
4
-
8
=
-
3
2
∴
Slope of ON
=
2
3
∵
Product
of
slopes
=
-
1
Equation of ON:
y
-
0
=
2
3
x
-
0
y
=
2
3
x
... (1)
Equation of BM:
x = 4 ... (2)
On solving equations (1) and (2), we get
4
,
8
3
as the coordinates of the orthocentre.
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Write the coordinates of the orthocentre of the triangle formed by points (8, 0), (4, 6) and (0, 0).