Question

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)

Answer 1

The answer to the question is C. the simplest method to ever solve for a dilation is by multiplying the axis by the factor. like in your question, the X(7,2), should be multiplied by the scale factor 1/4. You, first of all, multiply the x-axis(7) by 1/4=7*1/4=7/4. then you multiply the y-axis(2) by 1/4=2*1/4=1/2.After multiplying, the X coordinate would be(7/4,1/2). then solve for the other coordinates and the answer would be C. This is the simplest way to solve for dilation. 

Answer 2

Answer: 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

`s=(1)/(4).`

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

`X(7,2)~~~\Rightarrow~~~\left(7*(1)/(4),2*(1)/(4)\right)=\left((7)/(4),(1)/(2)\right),\\\\\\Y(-3,8)~~~\Rightarrow~~~\left((-3)*(1)/(4),8*(1)/(4)\right)=\left(-(3)/(4),2\right),\\\\\\Z(-4,6)~~~\Rightarrow~~~\left((-4)*(1)/(4),6*(1)/(4)\right)=\left(-1,(3)/(2)\right).`

Thus, the required location of the dilation is the new triangle with vertices
`\left((7)/(4),(1)/(2)\right),`
`\left(-(3)/(4),2\right)` and
`\left(-1,(3)/(2)\right).`

Option (C) is CORRECT.