Question

find the orthocentre of a triangle of vertices X+y+10=0,x-y-2=0,2x+y-7=0​

Answer 1

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