The segment joining p1(-4,-7)and p2(6,9)is divided in to four equal parts find the points of division
the x-distance from p1 to p2 is
... 6 - -4
the y-distance from p1 to p2 is
... 9 - -7
divide the distances by 4 to find the "length" of each step
start at p1 and add consecutive steps to find the 3 division points
To find the points of division, we first need to find the length of the segment joining p1 and p2. We can use the distance formula for this:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Let's plug in the coordinates of p1(-4, -7) and p2(6, 9):
d = √((6 - (-4))^2 + (9 - (-7))^2)
Simplifying this expression:
d = √(10^2 + 16^2)
d = √(100 + 256)
d = √356
Now that we have the length of the segment, we can divide it into four equal parts. Each division will be 1/4th of the total length.
Length of each division = √356 / 4
To find the points of division, we will start from p1 and move along the line segment by the length of each division. We can calculate the coordinates of each point using the formula:
x = x1 + (i * (x2 - x1)) / 4
y = y1 + (i * (y2 - y1)) / 4
Where i = 1, 2, 3 for the three divisions.
Let's calculate the coordinates of each of the four points:
First division:
x = -4 + (1 * (6 - (-4))) / 4
y = -7 + (1 * (9 - (-7))) / 4
Second division:
x = -4 + (2 * (6 - (-4))) / 4
y = -7 + (2 * (9 - (-7))) / 4
Third division:
x = -4 + (3 * (6 - (-4))) / 4
y = -7 + (3 * (9 - (-7))) / 4
Fourth division:
x = -4 + (4 * (6 - (-4))) / 4
y = -7 + (4 * (9 - (-7))) / 4
Now you can substitute these values to find the actual coordinates for each division point.