What is the missing coordinate y of the midpoint (2,y )of segment that passes through the points (x,3) and (-1,5)?
To calculate the coordinates x and y, we'll write the equation of the segment whose endpoints are the given points.
(xB - xA)/(x-xA) = (yB-yA)/(y-yA)
We'll substitute the coordinates for A and B:
(-1-x1)/(x-x1) = (5-3)/(y-3)
(-1-x1)/(x-x1) = 2/(y-3)
We'll cross multiply and we'll get:
2x - 2x1 = -y + 3 - y*x1 + 3x1
We'll move all terms to the left side:
2x - 2x1 + y - 3 + y*x1 - 3x1 = 0
We'll combine like terms:
2x + y(1 + x1) - 5x1 - 3 = 0
We know that (2,y) is the midpoint of the segment:
xM = (x1-1)/2
2= (x1-1)/2 => x1 - 1 = 4 => x1 = 5
yM = (3+5)/2
yM = (8)/2
yM = y = 4
The missing coordinate of the midpoint of the segment that is passing through the given points is y = 4.