Point d(-3.5) is a vertex of triangle def. after a rotation of the triangle about the origin, d' is located at (3,-5).which of the following was the rotation of the triangle?

note: it doesn't matter if its clockwise or counterclockwise when it comes to 180 degree rotations.

Explanation:

The rule for 180 degree rotations is

(x,y) ---> (-x, -y)

So the x and y coordinates flip in sign from positive to negative, or vice versa.

Point D ' (-3, 5) rotates to D ' (3, -5) following this rule

A further detailed break down might look like this

x = -3 becomes -x = -(-3) = 3

y = 5 becomes -y = -5

(-3, 5) > (3, -5)

if the eqn of the parabola is f(x) = (x-4)(x+2), we need to mult. this out to find the coordinates of the vertex.

then f(x) = x^2 + 2x - 4x - 8, and f(x) = x^2 - 2x - 8.

one way in which you can find the vertex is to calculate x = -b / (2a).   here, that comes to

        )

x = = 1.   f(1) = 1^2 - 2(1) - 8 = - 9.   vertex is at (1, -9).

        2(1) 

find another point on the curve:   let x=0, for which y=-8.   then (0, -8) is on the curve.   plot the vertex and this point and draw a smooth parabola thru both.

hope this

to find the total number of combinations, multiply the quantity of each item by each other:

2 pairs of shoes x 3 pairs of shorts = 6 different combinations.