Question

Use the Midpoint Formula three times to find the three points that divide the line segment joining (x1, y1) and (x2, y2) into four parts

Answer 1

To divide the line segment into four parts using the Midpoint Formula, find the midpoint of the line segment twice.

Step-by-step explanation:

To find the three points that divide the line segment joining (x1, y1) and (x2, y2) into four parts using the Midpoint Formula, you need to find the midpoint of the line segment twice. First, find the midpoint between (x1, y1) and (x2, y2), let's call it (x3, y3). Then find the midpoint between (x1, y1) and (x3, y3), which will be the first division point. Next, find the midpoint between (x3, y3) and (x2, y2), which will be the second division point. Finally, the fourth division point will be (x3, y3). Make sure to substitute the x and y values correctly in the midpoint formula to obtain the coordinates of the division points.

Answer 2

We are given points
`A(x_1,y_1)` and
`B(x_2,y_2)`.

We first find the midpoint M, of AB, which divides the segment AB into 2 equal parts,

then we find the midpoint N of AM, and midpoint K of MB.

Thus each of the half parts is divided into 2 equal parts. The whole segment is divided into 4 equal parts.




The coordinates of M, N and K are found as follows:


the coordinates of M are:
`( (x_1+x_2)/(2) , (y_1+y_2)/(2))`


the coordinates of N are:


`\displaystyle{( (x_1+(x_1+x_2)/(2))/(2) , (y_1+(y_1+y_2)/(2))/(2))=( ((2x_1+x_1+x_2)/(2))/(2) , ((2y_1+y_1+y_2)/(2))/(2))`


`=\displaystyle{((3x_1+x_2)/(4), (3y_1+y_2)/(4))}`


similarly, the coordinates of k are:


`=\displaystyle{((x_1+3x_2)/(4), (y_1+3y_2)/(4))}`