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).

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) = - 5/33(k + 3) = -5(k - 5)3k + 9 = - 5k + 253k + 5k = 25 - 98k = 16k = 2

So the answer is 2

F= 34 degrees (alternate angles are equal)

To find D

we first have to find the angles at AB

B =180- 165 (sum of angles on a straight line = 180°)

therefore B = 15°(we'll use this to find the angle at E)

A=34 (from the diagram)

so,

D = 180- (15 + 34) [sum of angles in a triangle = 180°]

D = 131°

E=15° (alternate angles are equal )

Step-by-step explanation:

there u go!