Point p lines on line MN and is 3/4 of the way from M and N. What are the coordinates of point P? M is at (-3,7) and N is at (9,15). Find point P
Wondering how a point on a line can be 3/4 from each end?
Assuming MP = 3/4 MN.
M(-3, 7), P(x, y), N(9, 15).
x + 3 = 3/4(9+3).
4x + 12 = 36,
X = 6.
y-7 = 3/4(15-7).
4y - 28 = 24,
Y =
To find the coordinates of point P, we can use the concept of midpoint formula.
The midpoint formula states that the coordinates of the midpoint between two points (x1, y1) and (x2, y2) can be found by taking the average of the x-coordinates and the average of the y-coordinates.
In this case, point M is located at (-3, 7) and point N is located at (9, 15). We want to find the coordinates of point P, which lies 3/4 of the way from M to N.
First, we need to find the coordinates of the midpoint between M and N. We can find the midpoint by using the midpoint formula:
Midpoint x-coordinate = (x1 + x2) / 2
Midpoint y-coordinate = (y1 + y2) / 2
Plugging in the values, we get:
Midpoint x-coordinate = (-3 + 9) / 2 = 6 / 2 = 3
Midpoint y-coordinate = (7 + 15) / 2 = 22 / 2 = 11
So, the coordinates of the midpoint between M and N are (3, 11).
Now, to find the coordinates of point P, which is 3/4 of the way from M to N, we need to find 3/4 of the distance between M and the midpoint.
To do this, we calculate the differences in x and y coordinates between M and the midpoint, and then multiply those differences by 3/4:
Difference in x coordinates = (3 - (-3)) = 6
Difference in y coordinates = (11 - 7) = 4
Coordinates of P = (Midpoint x-coordinate + (3/4) * Difference in x coordinates, Midpoint y-coordinate + (3/4) * Difference in y coordinates)
Plugging in the values, we get:
Coordinates of P = (3 + (3/4) * 6, 11 + (3/4) * 4)
= (3 + 9/4, 11 + 3/4)
= (3 + 2.25, 11 + 0.75)
= (5.25, 11.75)
Therefore, the coordinates of point P are (5.25, 11.75).