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

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justaguide | College Teacher | (Level 2) Distinguished Educator

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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.

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