Question

find the orthocenter of the triangle whose sides are given by x+ y+10=0, x- y-2=0 , 2 x+ y-7=0​

Answer 1

x + y + 10 = 0

solve for x

x + 10 = - y

x = - y - 10

solve for y

y + 10 = - x

y = - x - 10

x - y - 2 = 0

solve for x

x - 2 = y

x = y + 2

solve for y

- y - 2 = - x

- y = - x + 2

- y = 2 - x

- y/ - 1 = 2 - x / - 1

y = 2 - x / - 1

y = x - 2

2x+ y - 7 = 0

solve for x

2x - 7 = - y

2x = - y + 7

2x = 7 - y

2x / 2 = 7 - y

x = 7 - y / 2

solve for y

y - 7 = - 2x

y = - 2x + 7