The midpoint of ef is point p at (−6,−2). if point e is at (2,−4), what are the coordinates of point f?
a) (−14,0)
b) (−10,−8)
c) (−5,3)
d) (−2,−3)

Option A is correct answer.

Step-by-step explanation:

Midpoint formula is given by

        x =

         y =

         Here E = (2,-4)

so x1 = 2 and y1= -4

 x = -6 and y = -2  are given

therefore using above mid point formula

-6 =

-6X2 = 2+x2

-12 = 2+x2

x2 = -12-2 = -14

Likewise

-2   =

-2X2 =  -4 +y2

-4 = -4 +y2

y2 = 0

therefore Coordinate for point F will be (-14,0)

let f (x ) is a function and c be a positive real number,   the graph of the function g (x ) = f (cx ) is represented as follows.

when, c > 1,   the function compresses it in the x - direction.

when, 0 < c < 1, the function stretches it.

the function is g ( x ) = (9x )2.

the heighest power of x in g ( x ) = (9x )2 is 2, so the parent function is square function.

the equation of parent function is f ( x ) = x 2 .

the function is g ( x ) = (9x )2 and the parent function is f ( x ) = x 2 .

so, the functions f and g have the following relationship.

g ( x ) = f ( 9x ).

compare the function g ( x ) = f ( 9x ) with g (x ) = f (cx ).

c = 9 ( > 1 ).

so, the function g (x ) = (9x )2 compresses it in the x - direction.

step-by-step explanation:

good luck on ur quiz test or homework. have a good day : )