Respuesta :

mhanifa

Answer:

k = 2

Step-by-step explanation:

  • Perpendicular lines have slopes opposite reciprocal

Formula to find a slope:

  • m = (y₂-y₁)/(x₂-x₁)

Coordinates of the first line:

  • (k-1, k+2) and (4, -1)

Coordinates of the second line:

  • (-3, 2) and (2, 5)

Slopes of the lines:

  • m₁ = (-1 - k -2)/(4 - k + 1) = - (k + 3)/-(k -5) = (k + 3)/ (k - 5)
  • m₂ = (5 - 2)/ (2 + 3) = 3/5

Since m₁ = - 1/m₂, we have:

  • (k + 3)/ (k - 5) = - 5/3
  • 3(k + 3) = -5(k - 5)
  • 3k + 9 = - 5k + 25
  • 3k + 5k = 25 - 9
  • 8k = 16
  • k = 2

So the answer is 2

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