The midpoint of the linesegment from P1 to P2 is (-4, 1). If P1 equals (-4,6)what is P2?
Any help would be great.
> The midpoint of the linesegment from P1 to P2 is (-4, 1). If P1 equals (-4,6)what is P2?
Find the distance between P1 and the midpoint:
P1 - midpoint
(-4,6) - (-4, 1)
Start with the "x" coordinates. Since the "x" coordinate is the same (x = -4) for both P1 and the midpoint, we know the line is vertical. P2's
"x" coordinate will also equal -4.
Next subtract the "y" coordinates:
P1 - midpoint
6 - 1 = 5
The distance between P1 and the midpoint is 5 coordinate points.
Next subtract 5 from the midpoint's "y" coordinate to find P2.
midpoint - 5
1 - 5 = -4.
P2 = (-4, -4)
To find the coordinates of point P2, given that the midpoint of the line segment from P1 to P2 is (-4, 1), you can use the midpoint formula:
Midpoint formula: Midpoint = ((x1 + x2)/2, (y1 + y2)/2)
Here, P1 = (-4, 6) and the midpoint = (-4, 1).
Let's substitute these values into the formula:
(-4, 1) = ((-4 + x2)/2, (6 + y2)/2)
Next, we solve for x2 and y2.
For x-coordinate:
-4 = (-4 + x2)/2
Multiply both sides by 2:
-8 = -4 + x2
Add 4 to both sides:
-4 = x2
So, the x-coordinate of P2 is -4.
For y-coordinate:
1 = (6 + y2)/2
Multiply both sides by 2:
2 = 6 + y2
Subtract 6 from both sides:
-4 = y2
So, the y-coordinate of P2 is -4.
Thus, P2 = (-4, -4).