line segment AB has coordinates (-2, 1) and (6, 3)
find the coordinates of the three points that divide the segment AB into four equal parts
find the midpoint of AB, call it M
M is ((-2+6)/2,(1+3)/2) = (2,2)
now repeat the process by finding the midpoint of AM and BM
thanks!
To find the coordinates of the three points that divide the line segment AB into four equal parts, we need to determine the distances between the two given points and then divide those distances by four.
Let's begin by finding the distance between the coordinates (-2, 1) and (6, 3) using the distance formula:
Distance = √[(x2 - x1)² + (y2 - y1)²]
First, let's calculate the x-coordinate difference: (6 - (-2)) = 8
Then, let's calculate the y-coordinate difference: (3 - 1) = 2
Now, we can find the distance using the formula:
Distance = √[(8)² + (2)²]
Distance = √(64 + 4)
Distance = √68
Distance ≈ 8.2462
To divide the line segment AB into four equal parts, we need to divide the distance between the two points by 4:
Segment length ÷ 4 = 8.2462 ÷ 4 = 2.0616
Now that we have the length of each segment, we can calculate the coordinates of the three points that divide AB equally.
Starting from point A (-2, 1), we can move along the line segment AB by multiplying the segment length by the number of segments we want to divide it into.
1st point: (-2, 1) + (2.0616, 0) = (0.0616, 1)
2nd point: (0.0616, 1) + (2.0616, 0) = (2.1232, 1)
3rd point: (2.1232, 1) + (2.0616, 0) = (4.1848, 1)
Therefore, the coordinates of the three points that divide the line segment AB into four equal parts are:
(0.0616, 1), (2.1232, 1), and (4.1848, 1).