Question

Find the coordinate of three points that divide the line segment P(-4,7) and P (10,-9) into four parts of equal length

Answer 1

To find the coordinates of the three points that divide the line segment into four equal parts, we need to find the midpoints.

The midpoint of the line segment connecting P(-4,7) and P(10,-9) is given by the formula:

Midpoint = ( (x1 + x2) / 2 , (y1 + y2) / 2 )

Where (x1, y1) = (-4, 7) and (x2, y2) = (10, -9)

So the midpoint is:

Midpoint = ( (-4 + 10) / 2 , (7 + (-9)) / 2 )
= (6 / 2 , -2 / 2)
= (3, -1)

Now, we can find the midpoint of the line segment connecting P(-4, 7) and the previously found midpoint (3, -1):

Midpoint = ( ( -4 + 3 ) / 2 , (7 + (-1)) / 2 )
= ( -1 / 2 , 6 / 2 )
= ( -0.5 , 3 )

Now, we can find the midpoint of the line segment connecting the previously found midpoint (3, -1) and P(10, -9):

Midpoint = ( ( 3 + 10 ) / 2 , ( -1 + (-9) ) / 2 )
= ( 13 / 2 , -10 / 2 )
= ( 6.5 , -5 )

So the coordinates of the three points that divide the line segment into four equal parts are:
P1 (-4, 7)
P2 (-0.5, 3)
P3 (3, -1)
P4 (6.5, -5)
P5 (10, -9)