the midpoint of the line segment from p1 to p2 is (-1,3). if p1=(-6,7) what is p2?
(-1,3) = (-6,7) + (5,-4)
so, p2 = (-1,3) + (5,-4) = (4,-1)
To find the coordinates of point P2, which is the other endpoint of the line segment, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint between two points (P1 and P2) can be found by averaging the corresponding coordinates.
Let's denote the coordinates of P2 as (x2, y2). The coordinates of the midpoint are given as (-1, 3). By applying the midpoint formula, we can set up the following equations:
x-coordinate: (x1 + x2) / 2 = -1
(-6 + x2) / 2 = -1
Solving this equation, we can isolate x2:
-6 + x2 = -2
x2 = -2 + 6
x2 = 4
Now, let's find the y-coordinate using the same formula:
y-coordinate: (y1 + y2) / 2 = 3
(7 + y2) / 2 = 3
Solving this equation, we can isolate y2:
7 + y2 = 6
y2 = 6 - 7
y2 = -1
Therefore, the coordinates of P2 are (4, -1).