Question

Find k so that the line through(k-1,k+2) and (4,-1) is perpendicular to the line through (-3,2) and (2,5).

Answer 1

k = 2

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