A segment has endpoints m(5, -2) and n(-1, -2). After a dilation with center(0,0), M'(10,-4), and N'(-2,-4). If the scale factor is 3x+2, then which of the following is the value of x?

a) 0
b)1
c)2
d)3

1.A,D

2.B
3.B
4.B
5.A
6.D
7.C
8.A
9.D
10.C,F

looks like the line segment was doubled

scale factor is two

Vroom is right! Just took the test 100%

Vroom is RIGHTTT

To solve this problem, we need to understand the concept of dilation and how it affects the coordinates of the points on a segment.

Dilation is a transformation that changes the size of an object without changing its shape. It is performed by multiplying the coordinates of each point by a scale factor. In this case, the center of dilation is at (0,0), and the scale factor is given as 3x+2.

First, let's calculate the coordinates of the image points M' and N'.

To find the x-coordinate of M', we multiply the x-coordinate of M by the scale factor: (5) * (3x+2) = 15x + 10.

To find the y-coordinate of M', we multiply the y-coordinate of M by the scale factor: (-2) * (3x+2) = -6x - 4.

So, the coordinates of M' are (15x + 10, -6x - 4).

Similarly, for point N':

x-coordinate of N' = (-1) * (3x+2) = -3x - 2.
y-coordinate of N' = (-2) * (3x+2) = -6x - 4.

So, the coordinates of N' are (-3x - 2, -6x - 4).

Now, we compare the coordinates of M' and N' with the given values:

M'(10, -4) => x-coordinate: 15x + 10 = 10, which gives 15x = 0 => x = 0.

Since x = 0 satisfies the condition, the answer is option a) 0.