Respuesta :

mhanifa

Answer:

  • k = 18

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Given

Line 1

  • 3x - ky + 7 = 0

Line 2

  • Passing through the points (4, 3) and (5, - 3)

To find

  • The value of k, if the lines are perpendicular

Solution

We know the perpendicular lines have opposite reciprocal slopes, that is the product of their slopes is - 1.

Find the slope of line 1 by converting the equation into slope-intercept from standard form:

Info:

  • standard form is ⇒ ax + by + c = 0,
  • slope - intercept form is ⇒ y = mx + b, where m is the slope

  • 3x - ky + 7 = 0
  • ky = 3x + 7
  • y = (3/k)x + 7/k

Its slope is 3/k.

Find the slope of line 2, using the slope formula:

  • m = (y₂ - y₁)/(x₂ - x₁) = (-3 - 3)/(5 - 4) = - 6/1 = - 6

We have both the slopes now. Find their product:

  • (3/k)*(- 6) = - 1
  • - 18/k = - 1
  • k = 18

So when k is 18, the lines are perpendicular.

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