(2) Find the orthocentre of the triangle
whose sides are given by x + y + 10 = 0,
X-y-2 = 0 and 2x + y-7 = 0
Answers
(-4 , - 6) is orthocenter of the Triangle formed by the lines x + y + 10 = 0, X-y-2 = 0 and 2x + y-7 = 0
Step-by-step explanation:
x + y + 10 = 0,
X-y-2 = 0
2x + y- 7 = 0
Vertex of these two sides
x + y + 10 = 0,
X-y-2 = 0
x = -4
y = -6
(-4 , -6)
altitude from (-4 , -6) on 2x + y- 7 = 0 > Y = - 2x + 7
slope = -1/(-2) = 1/2
y = x/2 + c
-6 = -2+ c
=> c = -4
y = x/2 - 4
2y = x - 8
now similarly
Vertex of these two sides
X-y-2 = 0 and 2x + y-7 = 0
x = 3 , y = 1
(3 , 1)
Altitude on x + y + 10 = 0, => y = -x - 10
Slope of altitude = 1
y = x + c
1 = 3 + c
=> c = - 2
y = x - 2
2y = x - 8
y = x - 2
x = -4 , y = -6
(-4 , - 6) is orthocenter of the Triangle formed by the lines x + y + 10 = 0,
X-y-2 = 0 and 2x + y-7 = 0
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