Vertex a in quadrilateral abcd lies at (-3, 2). if you rotate abcd 180° clockwise about the origin, what will be the coordinates of a′ of the rotated quadrilateral a′b′c′d′?

The coordinate of A' after rotated through 180° is (3,-2)

Step-by-step explanation:

Given vertex A in a quadrilateral ABCD lies at (-3,2). Now we have to rotate the quadrilateral ABCD  180° clockwise about the origin.

The  point (x,y) is when rotated about the origin through 90° in clockwise direction then the new position will be (y,-x).

Now,the point A which is given is (-3,2)

First after rotation through 90° the new point will be (2-(-3)) = (2,3)

Again this point further rotated through 90° or we can say that rotation after 180° then the new point become A' =  (3,-2).

Hence, The coordinate of A' after rotated through 180° is (3,-2)

step-by-step explanation:

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1