Homework Help

What kind of triangle do the lines x+y+4 = 0, x-y-4 = 0, and x+4 = 0

user profile pic

xetabeta | Student, Kindergarten | Salutatorian

Posted June 7, 2012 at 4:47 PM via web

dislike 2 like

What kind of triangle do the lines x+y+4 = 0, x-y-4 = 0, and x+4 = 0

1 Answer | Add Yours

user profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted June 7, 2012 at 5:01 PM (Answer #1)

dislike 1 like

The three lines forming the triangle are x+y+4 = 0, x-y-4 = 0, and x+4 = 0.

x+y+4 = 0 has a slope of -1 and intersects x + 4 = 0 at (-4, 0)

x - y - 4 = 0 has a slope of 1 and intersects x + 4 = 0 at (-4, -8)

The lines x+y+4 = 0 and x-y-4 = 0 are perpendicular to each other.

They intersect at the point (0, -4)

The distance between (0, -4) to (-4, 0) is `sqrt(16 + 16) = 4*sqrt 2` . The distance between (0, -4) and (-4, -8) is `sqrt(16 + 16) = 4*sqrt 2`

The triangle formed by the three lines is an isosceles right triangle.

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes