The diagram shows MN segment graphed on a coordinate plane. Point P lies on MN segment and is 3/4 of the way from M to N. What are the coordinates of the point P?
these are points on graph M(-4, 4), N(6,-2)
M(-4,4), P(x,y), N(6,-2).
x - (-4) = 3/4(6 - (-4).
x + 4 = 3/4(6+4).
X + 4 = 30/4 = 7 1/2.
X = 7/2 = 3 1/2 = 3.5
y-4 = 3/4(-2-4).
y-4 = -18/4 = -4 1/2.
Y = -1/2 = -0.5
P(3.5,-0.5).
Can you explain why you used this equation please?
Well, it looks like Point P has found itself in a puzzling position! Let's see if we can navigate the coordinate plane together and find its coordinates.
We know that Point P is 3/4 of the way from M to N. So, if we imagine dividing the distance between M(-4, 4) and N(6, -2) into four equal parts, Point P would be nestled cosily in the third part.
To calculate the coordinates of Point P, let's start with the x-coordinate. The distance between -4 and 6 is 10 units, and 3/4 of that distance is 7.5 units. Since we're moving from -4 towards 6, we add 7.5 units to -4, giving us an x-coordinate of 3.5.
Now let's focus on the y-coordinate. The distance between 4 and -2 is 6 units, and 3/4 of that distance is 4.5 units. Since we're moving from 4 towards -2, we subtract 4.5 units from 4, resulting in a y-coordinate of -0.5.
So, after some fancy calculations, we find that the coordinates of Point P are (3.5, -0.5). Voila!
To find the coordinates of point P, we need to find the coordinates that are three-fourths of the way from point M to point N.
First, let's find the difference between the x-coordinates and y-coordinates of M and N:
Δx = x-coordinate of N - x-coordinate of M = 6 - (-4) = 10
Δy = y-coordinate of N - y-coordinate of M = -2 - 4 = -6
Next, let's find three-fourths of Δx and Δy:
Three-fourths of Δx = (3/4) * Δx = (3/4) * 10 = 7.5
Three-fourths of Δy = (3/4) * Δy = (3/4) * (-6) = -4.5
Now, we can find the x-coordinate of point P by adding three-fourths of Δx to the x-coordinate of M:
x-coordinate of P = x-coordinate of M + Three-fourths of Δx = -4 + 7.5 = 3.5
Similarly, we can find the y-coordinate of point P by adding three-fourths of Δy to the y-coordinate of M:
y-coordinate of P = y-coordinate of M + Three-fourths of Δy = 4 + (-4.5) = -0.5
Therefore, the coordinates of point P are (3.5, -0.5).
To find the coordinates of point P, which is 3/4 of the way from point M to point N, we can follow these steps:
1. Calculate the horizontal distance (change in x) and vertical distance (change in y) between points M and N.
- Horizontal distance: Δx = x2 - x1 = 6 - (-4) = 10
- Vertical distance: Δy = y2 - y1 = -2 - 4 = -6
2. Determine 3/4 of the horizontal and vertical distances.
- 3/4 of Δx: (3/4) * 10 = 7.5
- 3/4 of Δy: (3/4) * -6 = -4.5
3. Starting from the coordinates of point M (-4, 4), add 3/4 of the horizontal distance to the x-coordinate and 3/4 of the vertical distance to the y-coordinate.
- x-coordinate of P: -4 + 7.5 = 3.5
- y-coordinate of P: 4 + (-4.5) = -0.5
Therefore, the coordinates of point P are (3.5, -0.5).