s points) Given the two points P2,4) and Qu,-5) (a) Find the distance between P and...

s points) Given the two points P2,4) and Qu,-5) (a) Find the distance between P and Q (b) Find the midpoint of the segment joining P and Q. (c) Find the slope of the line through P and Q. (d) Determine an equation of the line through P and Q (e) Find an equation of a line perpendicular to the line in part (d) through (5,7). (f) Find the equation of a horizontal line through P.

P = ( - 2 , 4 ) , Q = ( 1, - 5)

a) distance = sqrt [ ( - 5 - 4)^2 + ( 1 + 2)^2 ]

distance = sqrt 90

distance = 3 sqrt 10

b) mid point = ( - 2 + 1 / 2 , 4 + 5 / 2 )

= (-1/2 , 9/2 )

c) slope = y2 - y2 / x2 - x1

= ( - 5 - 4 ) / ( 1 + 2 )

slope = - 3

d) equation of line

y - y1 = m ( x- x1 )

y - 4 = - 3 ( x+ 2 )

y = - 3x - 2

e) equation of perpendicular line

slope of perpendicular line = 1/3

y - 7 = 1/3 ( x- 5)

y = 1/3 x + 16/3

f) equation of horizontal line through P

y = 4

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