a right triangle is formed by the y-axis, the line y=2x+4,and another line. If the legs of the right triangle intersect at (2,8,) what is the equation of the other line of the triangle.?

Answer 1

If the LEGS intersect at (2, 8), then the y-axis must be the hypotenuse. That means the first leg is formed by y = 2x + 4 and since the legs always intersect at 90° in a right triangle, the second leg is perpendicular to y = 2x + 4 and goes through the point (2, 8).

The slope of the line y = 2x + 4 is "2" so the line perpendicular to that has a slope of -1/2 (perpendicular lines have slopes that are the negative reciprocals of each other). To find the line that has a slope of -1/2 and goes through (2, 8) you can use the point-slope form of a line:

y - y₁ = m(x - x₁) where (x₁, y₁) is (2, 8):

y - 8 = -1/2(x - 2)

y - 8 = -1/2x + 1

y = -1/2x + 9

Answer 2

If the legs of the right triangle intersect at (2,8) that is where the right angle is located. The point (2,8) is on the line y = 2x+4, so the equation of the other leg must be perpendicular to that line passing through (2,8).

The slope of the perpendicular will be the negative reciprocal of the slope of the line y = 2x+4.

Use y - y₁= m(x - x₁) to find the equation of that line.

After trying the above, confirm here:

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