find the coordinates of the three points that divide the line segment joining p( -4, 7 )& Q(10, -9) into four parts of equal length
The distance from P to Q is Q-P = (14,-16)
So starting at P, add 1/4, 1/2, 3/4 of that.
If the three new points are A,B,C, then
A = P + 1/4 (Q-P) = (-4,7) + (7/2,-4) = (-1/2,3)
Now do B and C in like wise.
Fake teacher, please stop. You will be banned for imitating a teacher.
or
take the midpoint of the 2 given points to have 2 new segments,
then take the midpoints of the two new segments.
PQ=y2-y1/x2-x1 so PQ= -9-7/10--4" 5.7
To find the coordinates of the three points that divide the line segment joining P(-4, 7) and Q(10, -9) into four equal parts, follow these steps:
Step 1: Find the length of the line segment.
Use the distance formula to calculate the length between points P and Q:
d = √((x2 - x1)^2 + (y2 - y1)^2)
= √((10 - (-4))^2 + (-9 - 7)^2)
= √((10 + 4)^2 + (-9 - 7)^2)
= √(14^2 + (-16)^2)
= √(196 + 256)
= √452
≈ 21.26 (rounded to two decimal places)
Step 2: Divide the length by 4 to determine the equal parts.
Each part would be the total length divided by 4:
part_length = 21.26 / 4
≈ 5.32 (rounded to two decimal places)
Step 3: Determine the direction and distance of each point.
Consider that the line segment has a certain direction: from P to Q. We need to find points that are at equal distances along this line segment.
Step 4: Calculate the coordinates of the three points.
To calculate the coordinates, we can use the concept of "internal division" of a line segment.
First point (P1):
The first point will be dividing the line segment into three parts, with the initial point being P. To calculate the coordinates of P1, we can consider using the formula:
x1 = (1/4) * (x2 - x1) + x1
y1 = (1/4) * (y2 - y1) + y1
Using the given coordinates:
x1 = (1/4) * (10 - (-4)) + (-4)
= (1/4) * (14) + (-4)
= 3.5 - 4
= -0.5
y1 = (1/4) * (-9 - 7) + 7
= (1/4) * (-16) + 7
= -4 + 7
= 3
The coordinates of the first point (P1) are (-0.5, 3).
Second point (P2):
The second point will be dividing the line segment into two parts, with the initial point being P1. To calculate the coordinates of P2, we can use the same formula as above, substituting P1 for P.
x2 = (1/4) * (x2 - x1) + x1
y2 = (1/4) * (y2 - y1) + y1
Using the coordinates of P1 (-0.5, 3):
x2 = (1/4) * (10 - (-4)) + (-0.5)
= (1/4) * 14 + (-0.5)
= 3.5 - 0.5
= 3
y2 = (1/4) * (-9 - 7) + 3
= (1/4) * (-16) + 3
= -4 + 3
= -1
The coordinates of the second point (P2) are (3, -1).
Third point (P3):
The third point will be dividing the line segment into one part, with the initial point being P2. To calculate the coordinates of P3, we can use the same formula again, substituting P2 for P.
x3 = (1/4) * (x2 - x1) + x1
y3 = (1/4) * (y2 - y1) + y1
Using the coordinates of P2 (3, -1):
x3 = (1/4) * (10 - (-4)) + 3
= (1/4) * 14 + 3
= 3.5 + 3
= 6.5
y3 = (1/4) * (-9 - 7) + (-1)
= (1/4) * (-16) + (-1)
= -4 - 1
= -5
The coordinates of the third point (P3) are (6.5, -5).
So, the coordinates of the three points that divide the line segment joining P(-4, 7) and Q(10, -9) into four equal parts are:
P1 (-0.5, 3)
P2 (3, -1)
P3 (6.5, -5)