Question

Find the orthocentre of the triangle whose sides are given by x + y +10=0, x-y-2 = 0 and
2x + y - 7 = 0.​

Answer 1

(-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