I have a question that does not make sense to me and would like some help with it. I don't need the answer, only the way to solve.

Question

I have a question that does not make sense to me and would like some help with it. I don't need the answer, only the way to solve.

It gives me a graph and asks me "what points would partition XY into segments with lengths having a ratio of 3:4?"

I can't share a grid, but here are the coordinates.

X = (-7), 12
Y= 7, -9

I'm just confused on the process of these questions, and I apologize to keep having to ask for answers on this site, but I can't reach any teachers due to the corona-virus outbreak in my area.

Thanks in advance :)

Answer 1

3 + 4 = 7 ... just divide the line into seven e

Answer 2

You have two points: (-7,12) and (7,-9)

x changes from -7 to 7, or 14
y changes from 12 to -9, or -21
You want a point P that is 3/7 of the way from X to Y. So,
P = X + 3/7 (Y-X) = (-7,12) + 3/7 (14,-21) = (-7,12)+(6,-9) = (-1,3)

Answer 3

I'm not sure what you mean? Please explain

Answer 4

Thanks a lot.

Answer 5

No problem, I'm here to help! To solve this question, you can use the concept of the section formula. The section formula can be used to find a point that divides a line segment into two segments in a given ratio.

The coordinates of point X are (-7, 12) and the coordinates of point Y are (7, -9).

To find a point that divides the line segment XY into segments with a ratio of 3:4, you can use the following steps:

1. Calculate the difference in x-coordinates and the difference in y-coordinates between points X and Y.
Δx = x2 - x1 = 7 - (-7) = 14
Δy = y2 - y1 = -9 - 12 = -21

2. Multiply the differences in coordinates by the desired ratio. In this case, the ratio is 3:4.
Δx_segment_1 = (3/7) * Δx = (3/7) * 14 = 6
Δy_segment_1 = (3/7) * Δy = (3/7) * (-21) = -9
Δx_segment_2 = (4/7) * Δx = (4/7) * 14 = 8
Δy_segment_2 = (4/7) * Δy = (4/7) * (-21) = -12

3. Add the respective changes in x and y-coordinates to the x and y-coordinates of point X to find the point that divides the line segment XY into the desired ratio.
X_segment_1 = (x1 + Δx_segment_1, y1 + Δy_segment_1)
X_segment_2 = (x1 + Δx_segment_2, y1 + Δy_segment_2)

So, to find the points that partition XY into segments with lengths having a ratio of 3:4, the first point would be:
X_segment_1 = (-7 + 6, 12 - 9) = (-1, 3)

And the second point would be:
X_segment_2 = (-7 + 8, 12 - 12) = (1, 0)

Therefore, the points that partition XY into segments with lengths having a ratio of 3:4 are (-1, 3) and (1, 0).

I hope this explanation helps you understand the process! Let me know if you have any further questions. Stay safe!