# What is the missing coordinate y of the midpoint (2,y )of segment that passes through the points (x,3) and (-1,5)?

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Student Comments

giorgiana1976 | Student

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.**