The midpoint of the line segment from P1 to P2 is (-1,3) if P1 is (-5,2) what is P2
The midpoint of (a,b) and (c,d) is
( (a+c)/2 , (b+d)/2) )
let P2 be (c,d)
for the x value :
(c + (-2) )/2 = -1
c -2 = -2
c = 0
find the y value of P2 in the same way.
Check by finding the midpoint of P1 and P2 using the formula I gave, and make sure you get the point (-1,3)
To find the coordinates of point P2, we can use the formula for finding the midpoint of a line segment. The midpoint formula states that the coordinates of the midpoint (M) of a line segment with endpoints P1(x1, y1) and P2(x2, y2) are given by:
M = ((x1 + x2) / 2, (y1 + y2) / 2)
In this case, we are given the coordinates of the midpoint (M) as (-1, 3) and one endpoint P1(-5, 2). We want to find the coordinates of the other endpoint, P2.
Let's substitute the known values into the formula:
(-1, 3) = ((-5 + x2) / 2, (2 + y2) / 2)
Now, we can isolate x2 and y2 by multiplying both sides of the equation by 2:
(-2, 6) = (-5 + x2, 2 + y2)
Next, let's separate the equations for x and y:
-2 = -5 + x2 [1]
6 = 2 + y2 [2]
Now, let's solve each equation separately:
From equation [1]:
x2 = -2 + 5
x2 = 3
From equation [2]:
y2 = 6 - 2
y2 = 4
Therefore, the coordinates of point P2 are (3, 4).