Triangle xyz where x(7, 2), y(-3, 8), and z(-4, 6) is dilated with a scale factor of one-fourth . where is the dilation located?
a. x’the coordinate (negative seven-fourths, one-half), y’the coordinate (three-fourths, negative 2and z’he coordinate (1, negative three-halves)
b. x’the coordinate (one-half, seven-fourths), y’the coordinate (2, negative three-fourthsand z’the coordinate (three-halves, negative 1)
c. x’the coordinate (seven-fourths, one-half), y’the coordinate (negative three-fourths, 2and z’the coordinate (negative 1, three-halves)
d. x’the coordinate (negative one-half, seven-fourths), y’the coordinate (negative 2, three-fourthsand z’the coordinate (negative three-halves, 1)

 The correct option is

(C) X coordinate (seven-fourths, one-half), Y coordinate (negative three-fourths, 2) and Z coordinate (negative 1, three-halves).

Step-by-step explanation:  Given that the triangle  XYZ where X(7, 2), Y(-3, 8), and Z(-4, 6) is dilated with a scale factor of one-fourth.

We are to select the correct location of the dilation.

We know that

if a point (x, y) is a vertex of a triangle, which is dilated with a scale factor of s, then the new co-ordinates of the vertex will be (sx, sy).

According to the given information, the scale factor of dilation is

So, the new co-ordinates of the image triangle after dilation are

Thus, the required location of the dilation is the new triangle with vertices and

Option (C) is CORRECT.

because they could drop even lower..

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