WILL GIVE BRANLIEST!!! Pls help! Determine the coordinates of the point on the straight line y=3x+1 that is equidistant from the

It could be either C or D, but I think C is the correct choice.

x    y
1     290
2    280
3    270
4    260
5    250
6    240
7    230
8    220
9    210
10  200
11    90
12  180
13  170
14  160
15  150
16  140
17  130
18  120
19  110
20 100
21    90
22   80
23   70
24   60
25   50
26   40
27   30
28   20
29   10
30   0

Response:

Congruent:  (x, y)→(x+3, y-4); (x, y)→(-x, -y)

Not Congruent:  (x, y)→(3x, 3y); (x, y)→(0.4x, 0.4y); (x, y)→(x/3, y/3)

Explanation in steps:

Transformations that yield congruent figures include translations, reflections, and rotations. In contrast, dilations result in figures that are not congruent.

The first transformation, (x, y)→(x+3, y-4), represents a translation 3 units right and 4 units down, leading to congruent figures since it merely shifts the figure.

The second transformation, (x, y)→(3x, 3y), indicates a dilation by a factor of 3, which enlarges the figure and therefore makes it non-congruent.

The third transformation, (x, y)→(0.4x, 0.4y), involves a dilation by a factor of 0.4, which shrinks the figure, leading to non-congruence.

The fourth transformation, (x, y)→(x/3, y/3), results in a dilation by a factor of 1/3, also shrinking the figure and rendering it non-congruent.

The fifth transformation, (x, y)→(-x, -y), reflects the figure, maintaining its size while modifying its orientation, thus ensuring congruence.

Let the number of years Brad has been on the soccer team be represented by x, and let y represent the number of years Scott has been on the same team.

From the information given, we formulate the equations:
5y - 2 = x -----(1)

x + y = 10 -----(2)

Now, substituting equation (1) into equation (2):
5y - 2 + y = 10
6y - 2 = 10
6y = 12
y = 2
Next, substituting this value back to find x:
x = 5×2 - 2
x = 8

So, Brad has spent a total of 8 years in the team.

By solving the equation -x+8+3x=x-6, we rearrange it to 2x+8=x-6. This leads to the simplification 2x-x=-6-8, yielding x=-14. The correct answer is letter B.